FINANCIAL STABILITY REGULATION THROUGH
MONETARY POLICY IN THE EURO AREA - HOW THE
EXISTENCE OF A WELFARE GAP CALLS FOR AN
EXTENSION OF CONVENTIONAL MONETARY POLICY
Robert Gremmer January 31, 2014
1. Introduction 2. Literature review 3. The model
(a) Agents in the economy i. Households
ii. Banks and money creation iii. Patient investors
(b) Private optimum (c) Social optimum
4. Externality and welfare analysis in the Euro area (a) Con nement of the periods
(b) Real risk-free and risky rates i. Real risk-free rate ii. Real risky rate (c) Parameters
(d) Welfare results
i. Baseline parameters with Euro area rates ii. Real-world Euro area parameters and rates 5. Sensitivity analysis
(a) Sensitivity analysis of the collateral constraint (b) Sensitivity analysis of the welfare eects
(c) Risky interest rate dynamics and excessive money creation 6. Monetary policy - a simulation exercise of the cap-and-trade approach 7. Critics and Discussion
Abstract
This Master thesis introduces a role for monetary policy to ensure market stability and to address the danger of welfare losses along the lines of Jeremy Stein (2011) and discussed by Stein and Kashyap (2012). When banks set up their capital structure, distinguishing between short-term money like debt and long-term debt, they do not internalize the adverse aect their choice of money creation has on re sale discounts in an adverse state of the economy. Furthermore a larger spread between riskless and risky rates makes short-term nancing relatively cheap, creating a strong incentive to engage in excessive money creation. Since a social planer or regulator recognizes this aect on re sales, he internalizes the externality and establishes a larger level of welfare. Hence the higher vulnerability of the banks leads to a welfare loss. Calibrating the model for the Euro area for the trial periods 2011 and 2012 under four dierent assumptions shows a welfare wedge for all assumptions. This is especially sensitive to changes in the riskless and risky rate. Conventional monetary policy by the ECB may be used to address nancial fragility by means of an cap-and-trade approach. Given a xed nominal interest rate, the ECB can change the interest on required reserves to control for nancial fragility. However, the estimates for this show that the model is not robust enough so as to produce reasonable values under calibrated parameters.
1. Introduction
Traditional views of monetary policy have emphasized its main role of price and - to some extent - output stability. While a central bank like the FED formulates the latter perspective as one of their two existing targets, the ECB puts special emphasis on price stability. Financial market stability as a principal goal has been left aside. In fact Europe's nancial market was merely subject to a decentralized system of national reg-ulatory institutions. Yet how the recent nancial crisis of 2007 has painfully revealed, national supervisors have proven unable to avert the creation and burst of the asset bubble that lead the crisis of 2007. Hence discussions have risen that the goals of in particularly the ECB must be revised so as to address the matter of nancial market stability in a more elaborate manner and to support any form of additional supervi-sion undertaken. The recent discussupervi-sion among economists has centered on aspects of macro-prudential regulation as the process of the Basle Accords demonstrates. This approach suggests a regulatory supervision rather than proactive monetary policy. Yet the question of interest is how a policy instrument of the ECB could ideally contribute to macro-prudential regulation.
Jeremy Stein (2011) (S2011 subsequently) provides one answer in this context. Tra-ditionally the di culty at the core of the discussion among economists lies in modeling the nancial fragility that may eventually lead to a crisis and warrant interaction by
a regulator. Stein (2011) takes on a new view on this matter. He designs a stylized three period partial equilibrium model in which the level of money creation (i.e. the short-term debt of a bank's liabilities) by banks create an externality that plays the crucial role in reinforcing nancial distress that may lead to a nancial crisis. More precisely, when money creation is unregulated, banks might choose a capital structure that deviates from the social optimum. Absent any internalization, such a market fail-ure represents a negative externality in the economy and can be crucial to nancial stability. Finally a welfare loss will arise when the spread between risky and riskless rates is su ciently large.
I will give a model-based analysis along the lines of the paper Jeremy C. Stein, `Monetary Policy as Financial-Stability Regulation', 2011, NBER working paper No. 16883 on how banks have an incentive to create a quantity of riskless money and engage in investments that exceed the social optimum. The trigger for such a wedge between the private and social optimum appears in the form of spreads between the short- and long-term equilibrium interest rates. When a bank chooses between cheap short-term nancing on the one hand side, or money creation, respectively, and long-term nancing on the other hand side, it will chose a capital structure that minimizes its nancing costs. Hence, the bigger is the spread between long-term and short-term nancing, the cheaper is the creation of money to the bank relative to the emission of long term bonds. Thus with higher spreads, banks have a stronger incentive to build up short term debt. The key channel for the welfare loss then operates through re sales of a bank's assets. In a stochastic environment, the bank has uncertain proceeds from its investments and therefore may not always be able to pay back its short-term debt. Consequently the bank has to re sale part of its assets at a discounted value to other investors. Crucially in this scenario: unlike the social planner, banks do not recognize the incremental costs that their choice of re sale assets has, and therefore refrain from internalizing this eect. This is why banks may create socially excessive money and back it up by increasing its assets through additional investments. Finally the interest rate spread has to be su ciently large in order to generate a welfare wedge. This concludes the theoretical exhibition of the model.
The motivation to estimate the predicted outcome of the model for the Euro area is its relevance. Currently, 17 countries share a common currency and succumb to the same monetary policy. In the light of such a large currency union, money matters and its relevance cannot be discussed away. A glimpse at the sheer absolute and relative size of monetary aggregates gives an idea of the size and hence of the relevance. As of December 2012 the nominal M1 level in the Euro area amounts toEUR 5,109.9bn. M2, which additionally entails deposits of agreed maturity of up to two years and deposits
redeemable at a period of notice up to three months, is almost twice the amount of M1, quoting atEUR 8.992,2 bn1. Comparing it with the Euro area GDP in 2012, amounting to EUR 8.625 bn, M1 and M2 have almost 60% and 104% the size of the GDP. Clearly any sort of excessive creation of short-term money-like debt by credit institutions can certainly be assumed to have non-negligable adverse eects on nancial stability.
In the light of the current macroprudential supervision, an interesting feature of the model and mechanics involved in it seems to draw a parallel to one of the essential tools of the Basel III Accords. In particularly the Liquidity Coverage Ratio is established so as to ensure the bank's capability to service short-term liquidity demand by a pool of high-quality assets in a stress scenario. The model distinguishes exactly between both short-term and long-term horizons and moreover features a stress scenario to which all banks are exposed. In fact the model in its nature takes the LCR for granted as the short-term demand is modelled to be serviced without a compromise. This leads to the interpretation that the model as such analyzes further nancial fragility issues which cannot be handled by the LCR. The crucial failure than seems to be hinged on the term high quality assets. In fact the model seems to imply that the representative investment opportunity for the bank is not completely a high-quality asset, otherwise the model would fail to provide a state-contingent stochastic mechanism. But the problem regarding nancial fragility is not the possibility of a loss through some fraction of low quality assets, rather it is the herding behavior of the banks. As introduced in the paragraph before, the aggregate supply of re sales creates the nancial fragility. So it can be concluded that the stress scenario as considered by the LCR appears not to play a role but is implied to be neutralized by the simple assumption, that short-term deposits (i.e. money) is riskless and all short-term claims are payed o, no matter how. In a similiar fashion S2011 seems to abstract away any problems that might occur from a breakage of the Net Stable Funding Ratio. This ratio looks at the ratio of available and required amount of stable funding, where the term stable describes long-term debt such as liability or equity that at least stays for a year in the bank in the event of a stress scenario. The pecularity of this ratio is that it assigns each asset class a certain weight (availability and required factor) along its risk and liquidity pro le. Carrying over this ratio to the model, the required funds apparently are pinned down by the amount of long-term investment. It can be assumed that this asset is weighted with a full 100% due to its long-term horizon. On the side of the available funding we observe that while long-term funding seems to enter the calculation with a full 100% (assuming
it belongs to Tier 1 and 2 capital instruments), short-term funding, if stable and from retailers, only enters with a weight of 85%. Following the ratio, we receive a result that is <1 and hence violates the NSFR. As a consequence, the denominator and hence the required funding must be reduced by incorporating an asset that has a factor smaller than one and such that the NSFR becomes >1. Given the three balance sheet items bank's investments, short-term and long-term funding in the underlying model, a fourth intuitive asset class could be cash. Holding cash enters with 0% and thus, if a little fraction of the money created is being held as cash, the bank might avert any violation of the NSFR. Yet regarding this paper the aforementioned three balance sheet items will not be supplemented by a fourth one, thus the NSFR is not scheduled to play a decisive role here, further analysis on this matter is left aside2.
In this analysis I want to nd out, what the implications of the model suggested in S2011 for the Euro area are, and, if there is a case for ancial stability, how could this be implemented? In particularly I want to detect whether a welfare loss exists, how sensitive the outcome responds to the choice of parameters and nally, how monetary policy can be redesigned to promote nancial stability. I will solve for the model suggested in S2011 and replicate the model for the Euro area on the grounds of real-world parameters. Accounting for the heterogeneity in market risk premia and risk-free interest rates I construct four dierent parameter sets regarding the pick of the riskless and risky rate, and replicate the model along these four settings. The sample periods are given by the two most recent and fully passed years, namely 2011 and 2012. Next I augment the model by providing a welfare analysis for the Euro area which was not carried out in S2011. Unlike Stein (2011) who has a oating or non- xed parameter determining the banks' return on their assets, I implement a xed scheme that ensures a xed calibrated return parameter. The central result is that the model predicts a welfare wedge for all four assumptions. Furthermore I introduce a sensitivity analysis in which I test for the sensitivity of the welfare outcomes with respect to the parameter choices. Another novelty that I introduce contrasts the role of the short-term rate in S2011. While in S2011 only the short-short-term rate drives the real interest rate spread,I additionally follow the assumption and intuition that the risky rate is the uctuating componenet that adjusts to risk perceptions. In order to highlight the role of monetary policy in this game, S2011 on the one hand develops a monetary policy based on microfoundations but relying on the scal theory of the price level. On the other hand Kashyap and Stein (2012) (KS2012 subsequently) oer an approach that has no microfoundation but a price level that is exogenously determined in the spirit of
a New-Keynesian model. I combine S2011 and KS2012 and show along their lines how the cap-and-trade approach as a monetary policy could be implemented in the Euro area. This looks very much like a market for certi cates, in which permits for money creation are assigned and made tradable, thereby producing a price of permits in this permit market. In a real setting a regulator targets the price in this market. Given asymmetric information, the regulator is likely to be unaware of the bank's investment opportunities. The cap-and-trade approach however makes this missing link redundant, allowing him to target the price in the presence of asymmetric information. In a setting denominated in nominal terms, the interest payed on reserves and the scarcity value, the dierence between this interest an the nominal interest rate along with the price for permits, lie at the core of this new policy. However I estimate unrealistically high recommendations for the these rates within the period 2011-2012. I nd that the policy rates are too sensitive to the permit price uctuations, indicating that a yet-to-be-found model extension might help to reduce the volatility.
2. Literature review
The idea of incorporating money into utility alongside consumption and leisure evolved from a crucial shortcomming of a standard neoclassical model. Literature agrees that money can buy goods and goods can buy money, but goods cannot buy goods, hence attributing value to a monetary medium of exchange.3 Such standard neoclassical models in the tradition of Ramsey (1928) or Solow (1956) used to abstract away from the importance of such a transaction process itself, usually done by transaction mediums like money. Instead it focused on a mere nonmonetary economy and did not incorporate any medium of exchange. The rst one to break with this tradition and ackowledge the use of money as a transaction medium were Baumol (1952) and Tobin (1956), who developped partial equilibrium models of transaction demand in which money depends on income, opportunity cost of holding money and the volume of transaction. These are the predecessors of the later developped cash-in-advance models. Such CIA-models explicitly capture the transaction demand for money. Two major concepts in the history of CIA-models are worth mentioning. On the one hand side, Lucas (1982) determines the asset market to open before the goods market. This way the agents can allocate their portfolio between assets and cash before they consume, knowing how much they actually want to consume. Thus they allocate their portfolio between assets and cash after observing the shock but before buying any good. On the other hand side Svenson (1985) reverses this sequence by determining the goods market to open before the asset market. Crucially in such a scenario, agents cannot allocate their portfolio in accordance to their consumption needs. As a consequence the agent might hold too much or to little cash balances and forego interest rate income. Paralleling this conceptual development, Patinkin (1965) picked up the idea of incorporating money balances into a utility function and thereby created a short-cut for the cash-in-advance concept. This way money yielded direct utility to the agent and made CIA-constraints redundant. Although this approach set the basis for the subsequent MIU-Models, his model fell short of capital accumulation. Sidrauski (1967) eliminated this shortcomming and introduced capital into his model, thereby augmenting his model by a crucial feature. It is noteworthy to mention, as Walsh (2010) points out in his discussion of monetary models, that, given suitable restrictions on the utility function, this new concept can guarantee that in equilibrium agents choose to hold positive amounts of money4, as money will be positively valued.
3see Clower (1967) 4see Walsh (2010), p. 34
Following a simple Taylor Rule as discussed by Taylor (1993), the nominal interest rate set by the central banks attempts to reduce output deviations and in ation gaps from their respective target level. What has traditionally been set aside in the loss function of central banks is the role of nancial markets. It was not until 2009 when the role of credit frictions prominently entered general equilibrium models in the spirit of New Keynesian DSGE models designed by Curdía-Woodford in 2009 and redisigned in a reduced version by Woodford in 2011. In the latter paper the loss function for the optimal monetary policy is augmented by a endogenously determined nancial dis-tortion measure which represents credit frictions accross heterogenous households and depends on a probability level that itself is determined by macroeconomic conditions. Furthermore, Del Negro et al. (2010) and Gertler and Karadi (2011) also analyze along the lines of an exogenously occuring nancial crisis the optimal conduct of monetary policy. Clearly these developments show that economic research has come to adopt with some delay a prominent role of nancial crisis in their models, recocknizing that in ation targeting alone is not su cient anymore to address modern monetary policy.
The link between modern DSGE models in the New Keynesian spirit and the model in Stein (2011) is to be seen in its (Stein's) partial equilibrium nature. Rather than looking at a general equilibrium, Stein and the academic work he builds on seek to isolate, carve out and model relations and mechanisms in a more profound way, so as to provide new impulses for the grounds of modern dynamic models - or even represent an add-on compatible with a dynamic setting (This fact will become clearer in paragraph 6.). A number of important contributions enter his model design.
The central banks' role in discussions about nancial market stability has been widely discussed. Chronologically Bagehot points out the function of central banks as a lender of resort in an attempt to lend early and freely (i.e. without limit) to solvent rms [...] so as to avoid a panic. In times of increasing nancial market integration and securitization, Goodhart (1988) asserted that competitive pressure in a milieu of limited information [...] would lead to procyclical uctuations punctuated by banking panics5, therefore making a convincing case for the creation of independent central banks. One of the rst attempts to capture externalities deriving from a bank's is-suance of short-term debt and hence money creation dates back to 1998. Gersbach (1998) analyzes the functioning of inside money creation in an overlapping generations model where allocative e ciency by oering short-term contracts is examined for both a competitive free banking and monopolistic banking industry. Although both indus-tries do not achieve a rst-best allocative solution, he nds that monopolistic banking
Pareto-dominates free-banking. Both scenarios feature banks that have an over incen-tive of money creation and do not internalize the resulting externality. In the model of Hart and Zingales (2011) the resulting externality from an ine cient over-issuance of money as a relatively save asset stems from the lack of a simultanous double co-incidence of wants. In this setting liquidity aects welfare through prices. In general however both models fall short on incorporating a relation to nancial stability.
The money-like characterics of bank deposits, underlying the model in Stein (2011), stems from the absence of adverse selection. Adverse selection in the form of het-erogenous degrees of information accross investors and hence informational advantages (i.e. private information) causes the asset value to change frequently. Intuititevely if investors are able to learn new information, they can bargain from this private infor-mation vis-à-vis the other investors. Gorton and Pennacchi (1990) argue that securities which split the cash ow of an underlying asset may help to reduce this asymmetric information. Bank deposits represent such a split up of an asset and hence act as an example of information-insensitive debt. Since the value of this liability rarely changes, bank deposits are very liquid and indeed money-like.
Moreover the main source on money creation in Stein (2011) stems from banks which are subject to bank regulation such as reserve requirements. However, as he points out, a range of short-term nancial intermediary liabilities display monetary services without being subject to a bank regulation scheme. In fact such regulation alone certainly is not caputuring all money-like liabilities in the nancial market - assuming that they did would be less realisitc as a description of modern advanced economies. Gorton (2010) recalls that the shadow banking system is at the heart of the current credit crisis, indicating that a substantial part of this private money creation results from the shadow banking system, i.e. outside the traditional regulated commercial banking sector. In particular the boosting demand for information-insensitive securities has increased, and the, along the lines of Gorton and Pennachhi (1990), the increasing securitization of loans into dierent tranches lie at the heart of the current crisis. Gorton and Metrick (2010) nd that the trenching of bank loans created information-insensitive bonds that have increasingly been used as collaterals in sale and repurchase transactions. In the wake of housing bubble burst and the shock to subprime mortgage values, these collaterals however have come to become information-sensitive, resulting in changes in values and reduction in liquidity. Hence depositors, observing this adverse eects on their collaterals, are increasingly requiring larger hair-cuts. Stein (2011) recognizes that monetary policy as conventionally practiced is generally not su cient and hence points out the special role of the model as it makes clear the circumstances under which monetary policy needs to be supplemented with other measures.
One of the core elements in Stein (2011) is the re sale mechanism that elicits nancial fragility and hence paths the way to a severe nancial crisis as banks run into nancial distress. Vishny and Shleifer (1992) capture the idea of an industry that suers from an adverse shock, which challanges the ability of rms to service the debt obligations by illuminating especially the buyer side of an economy or industry. When a distressed rm tries to sell assets, the potential buyers in the eonomy are likely to incur liquidity and funding problems as the shock is industry-wide. In the wake of such a break down of the demand side, the value of these assets is likely to drop even sharper, at prices below value at best use. Furthermore industry outsiders, which are likely to be not distressed, are able to buy these assets, but face private costs such as agency costs due to acquisition and managing costs (as they lack expertise and are not fully-informed about the proper valuation). This also explains why asset prices drop to prices below the value in best use. Stein (2009) analyzes the eect of the observed shift from private to shophisticated professional investors (naive investor vs. rational arbitrageur) on market e ciency. The principal question to answer is whether the increase in rational arbitrageurs eventually brings prices on average closer to their fundamental values and reduces the nonfundamental components of volatility. He controls for two factors: On the one hand he examines the role of crowding, i.e the situation in which an investors pursue the same strategy without knowing of and orchestrating their action. On the other hand the second factor relies on the mechanism that the choice of the private optimal leverage ratio by the arbitrageur can create a re sale externality, which in turn increases the probability of a nancial crash. This mechanism is somewhat analogous to the underlying distress mechanism in Stein (2011), in which large re sale discounts are not internalized and thus leave the banks overly vulnerable in an adverse state of the economy.
In a more elaborate way the re sale machism is discussed by Diamond and Rajan (2009). At the core of their analysis lie the incentives of both buyers and sellers of such assets (called Level 2 and Level 3) that are not frequently traded and for which the price was either based on models or largely hypothetical6. On the grounds of such assets, Diamond and Rajan (2009) aim at explaining why a term credit crunch (i.e. a large withdrawal of bank term deposits and accounts that results in a liquidity need) and a possession of large illiquid assets on a bank's balance sheet not only have the same origin but may even have explanatory power beyond the Crisis of 2007-2010.7. When a bank's customers withdraw a large amount of money from their term deposits and accounts, it may run into distress when it tries to service these demands but disposes of
6see Diamond & Rajan (2009), page 1 7see Diamond & Rajan (2009), page 2
too large an amount of illiquid assets such as mortgage backed securities. Because such assets are considered illiquid due to their little trading frequency and their character of being a highly sophisticated as well as specialized product only accessible to certain institutionalized agents, the buyer side of the market is potentially small. This way the bank sells its assets at a bid price that is smaller than its ask price, hence at re sale prices. The bank of course knows about the possibility of a sudden run on its term deposits and accounts and hence is aware of risk of not surviving8. Precautionary re sales (i.e. re sales before the liquidity need arises) help the bank to raise cash and keep cash balances over time. However, as Diamond & Rajan describe the incentive problem on the seller side, the management would perceive such a loss from re sales as fairly unfavorable because it losses pro ts. Such loss from re sales can stem from re sale prices which are irrationally low. In particularly when potential investors, who have cash resources to buy up these assets, know that future re sales are pro table for them, the precautionary re sales must yield about the same pro t for the investor to buy them, depressing its current value even further. This way the intertemporal trade-o for investors of potential precautionary re sales must be such that arbitrage possiblities are neutralized, making the investor indierent9. Then, from the point of the bank, holding on to the assets and speculating on the recovery of their prices from their (maybe) irrational level maintains the pro ts in the good states (i.e. if the bank does not incur a sudden liquidity demand and hence survives). Thus the bank prefers to save the pro ts rather than to preserve its stability in the future. This may eventually lead to a seller strike.
In contrast to Stein (2011), Diamon and Rajan (2009) determine the liquidity need to stem from stochastic term deposit and account withdrawal before introducing risky assets. In Stein (2011) the liquidity need stems entirely from risky assets while the cash withdrawal is not sudden but determined by the maturity of short-term deposits. Furthermore the distress of the banks is exacerbated by the aggregate sale of assets by all banks in the model.
Finally the calibration of the model requires a way of pinning down the (real)10 risky rate of return. One way of doing so is to look at the risk premium of large stock exchanges that list large, potentially diversi ed and well capitalized multinationals so as to abstract away from any risk other than the market risk (in particularly the inherent ideosyncratic risk, i.e. the risk of a particular asset or company). They conclude that in
8Fire sales always cannot entirely eliminate the risk of becoming insolvent.
9If the buyers were not indierent, they would most likely me on a buyer's strike, reluctant to buy the
assets now because future resales have a larger discount and hence yield a larger pro t.
10it does not necessarily have to be real because and average of in ation can be calculated so as to derive
a model that is not a Arrow-Debreu model (i.e. a model that features certain economic assumptions such as convex preferences, perfect competition and demand independence 11), is likely to not account for small risk-free rates and large historically measured risky rates (or equity return). The reason is that the risk aversion of agents is required to be implausibly high so as to account for a large spread between risky free (in the form of bonds) and equity return (in the form of stock returns). In the light of such a risk-premium driven analysis one has to always bare in mind the limitations of a model calibration as discussed by Mehra and Prescott (1985).
3. The model
The model features households and the nancial sector, which is represented by banks and patient investors. The time span covers three dates, namely t=0, t=1 and t=2. The economic agents are subsequently introduced.
a) Agents in the economy
i) The household Initially at t=0 households are endowed with some amount Y of a good, which is the only good existing in this real economy and thus equips households with wealth Y . They draw utility from consumption in t = 0 and t = 2, as well as from their holdings of monetary balances at t = 012. Here money yields utility because their money holdings as of t = 0 promise a secure consumption of M-units of the good in t = 2. Therefore money balances are discounted by γ. Furthermore the level of consumption at t is denoted as Ct and is discounted by β. Households' utility is given by
U = C0+ βE(C2) + γM (1)
At the same time the households can smooth their consumption through investing in a mix of nancial claims that are issued by banks. This mix consists of two options: On the one hand households can hold risky long-term assets, which yield expected proceeds RBfor consumption in t = 2. Since long-term bonds are risky, they do not guarantee secure consumption in t = 2. One the other hand households can invest in riskless short-term claims with certain proceeds of RM. Given their riskless nature, these claims entail the characteristics of money as a means of transferring a fraction of the initial endowment to the second period so as to consume it. In fact a key assumption here is that any privately created claim that promises secure time-two-consumption can provide monetary service as long as they are riskless.13
A third investment opportunity comes in the form of risky physical projects. How-ever since households do not possess monitoring expertise, they do not undertake these investments, but rather invest indirectly via banks through holding privately (i.e. by banks) issued nancial claims.14
A peculiarity in this model is that contrary to what standard economic analysis 12As will become clear shortly, the second period can be seen as an intermediate period where no goods are
consumed
13Households do not have a budget constraint because the model aims at illustrating externalities stemming
from a bank's maximization problem
14Households also invest some of their endowment into nancial market agents other then banks. In particular
suggests, the real interest rates RB and RM are not pinned down by quantities, i.e. by a demand and supply equilibrium of nancial claims. Given the linearity in intertemporal consumption, the household is risk-neutral. This festure determines the discount rates for the consumption from the two assets and therefore determines the real rate on these assets. Any utility from one unit of consumption that is derived from risky bonds correspond to β-units of time 0 consumption. Given the linearity, consumption from the risky asset is discounted with β. In an analog manner utility derived from one unit of consumption stemming from short-term claims in periods 2 is equal to consuming β +γunits in time zero units since utility derived from riskless monetary service adds an additional utility that is valued with γ. Hence the riskless and risky rate, respectively, become15
RM = 1
β + γ (2)
RB = 1
β, β + γ < 1 (3)
The striking feature here is that since the real rates are determined by the linear preferences of the households, they and the spread between them are independent of the quantities of money and bonds.
ii) The banks The second agent in this economy is represented by a continuum of identical banks with total mass of one. Banks do not have any initial endowment, so any amount of investment I undertaken must be raised externally. However, since they possess monitoring expertise, they have access to investment opportunities16. Hence, after raising funds by issuing short-term and long-term claims, they invest an amount I into physical projects. While long-term claims mature at time 2, short-term claims mature att = 1 and yield proceeds that are held by the household in the interim (before consumed) until time 2 is realized17. The nature of riskiness of these projects hinges on a public signal in t = 1, which reveals whether the good or bad state in the economy occurs in t = 2. With probability p, the good state sets in and banks earn investment proceeds f(I) > I, where f0(I) > 1 and f00(I) < 0 . However, with probability (1 − p) the bad state is realized. In this state of the economy, the overall proceeds have an
15Appendix 1 provides a derivation of these results
16Whereas in the real world banks would lend money to investors that in turn invest in those physical
projects, here the banks invest directly in physical projects. Thus the model abstracts away from contracting frictions and hence enables the bank to costlessly seize all proceeds from investment.
17It is not explicitly stated in the model whether the households hold the proceeds in cash or as a deposit
additional level of risk. With probability q a bank earns λI/q, but with probability of (1 − q)a banks earns 0. Thus banks expect their uncertain proceeds λI ≤ I in the bad state of the world. The parameterλ may re ect a measure for the market liquidity or other exogenous factors that negatively in uence the expected project proceeds.
Such a contingent setting implies that in the bad state of the world, the bank has trouble or is even unable to service short-term claims held by households. Suppose that the amount of investment nanced by short-term claims, i.e. money, is given by m ,then the total obligation M in period 2 is given by18
M = mIRM. (4)
In the more optimistic case of the bad state, banks are left with a positive fraction mof their initial investment. So in order to avoid a failure of the promise in the adverse state of the economy, it is required that
mIRM = M ≤ λI/q. (5)
Given the zero proceeds in the pessimistic outcome of the bad state, banks are bound to break the promise as they are not able to service M. The point to take away here is that upon receiving a bad signal, banks can only credibly ensure the riskfree-nature of money by selling a fraction 4 of their asset holdings at the discounted price k on the secondary market, where the only purchasers are patient investors. The discount value k is bounded within the range 0 ≤ k ≤ 1 . Thus a credible promise requires that in the bad state
k4λI = mIRM, (6)
that is, the proceeds from the asset sales just match the outstanding short-term debt. Since the maximum amount of assets, that can be sold, has an upper bound given by 4 ≤ 1, the fraction of investment nanced by money m, has an upper bound:
mmax = kλ
RM. (7)
This is the collateral constraint and states that the fraction of investment nanced through short-term claims must not be bigger than a threshold value which depends on the parameters k, λ and RM. As will become clear in the description of the patient investor, k plays a crucial role. Furthermore m increases as RMdecreases and hence the spread RB− RM widens. Finally this equations implies that as long as money creation
is not too large, privately created short-term debt can be made riskless.19
Given that banks have assets in form of physical projects I, they engage in maturity transformation activities only to the extent that they choose their capital structure. However money is a cheaper source of nancing than long-term bonds (recall that RM < RB), therefore the incentive to raise m is high.
iii) The patient investor Finally the introduction of the patient investor closes the model economy. Initially this intermediary is endowed with a xed amount of wealth W at time 1 which is supplied by the households. There is no optimization of the patient investors, and households are assumed to supply the xed amount of wealth as an investment yielding RB. The fact that wealth is xed and cannot be adjusted implies that wealth is independent of the realization of the state. As Stein highlights, the capital rigidity re ects slow-moving capital in the nancial world and ensures that patient investors cannot raise more capital upon receiving the signal about the state of the economy. All proceeds from investment will eventually accrue to the household. The scope of activity of these investors hinges on the realization of the state. In the good state they invest all their wealth W in new late-arriving investment projects that occur in the time 1 but are not available in time 0 yet. This real investment yields proceeds that feature diminishing marginal returns and are described by a concave function g(W ). Furthermore these yields are independent of the realization of the state. Yet when the bad state comes accross, the patient investors act as the counterparty on the secondary market for time-0-projects that are on the banks' balance sheet. In such a setting, the investors absorb all resold assets and use the remaining wealth for investments in time1 projects. One of the crucial elements in this model comes here into play. Given patient investors' outside option in the form of time-1 projects, the marginal return to investment of buying resold assets and time-1 investments must break-even. This is a necessary condition for the patient investors to have an incentive to absorb resold assets. The mechanism through which demand and supply of these assets are equilibrated operates through the discount value k. Let K = W − M be the amount invested in time-1 projects after having purchased sold assets (i.e. the re sales), then an equilibrium on the market exists if
1 k = g
0
(W − M ) = g0(K). (8)
19Usually the ideosyncratic risk of failure of an institution causes the assumption of a riskless short-term debt
issuance to fall. However it is assumed that banks chose portfolios such that they diversify away their risk of failure, ending up always with projects that yield a positive net present value. The diversi cation assumption is a necessary condition for the creation of riskless claims.
This equation states that the patient investor must be indierent between the gross return rate on the re sales from banks 1/k) and the marginal return from its investment in late arriving projects g0(K).
An increase in the amount of re sales (M), that are assumed to be absorbed by the patient investors, reduces the volume of time-1 investments and hence increases their marginal return. Absent any possibility of acquiring additional wealth, the assumption that the patient investors' capital is scarce enforces this trade-o. It follows that the gross rate of return 1/k has to increase, a movement that can only be achieved by a decrease in k. Thus changes in the price of re sales assets follow variations in the amount of re sales. In the presence of slow-moving capital, the marginal return to time1 projects becomes the hurdle rate in this game. In fact the preceding process illustrates the real cost of re sales, since a marginal increase in the amount of short-term nancing decreases the value of the assets when sold in the adverse state of the economy.
b) Private optimum
The optimization problem of the bank re ects its most innate business activity, namely maturity transformation. Banks choose optimal investment I and optimal capital struc-ture, that is, the optimal fraction m of short-term nancing. Three components make up the pro t function. First, assuming that the banks only issue long-term debt and refrains from short-term nancing, i.e. m = 0 , gives the expected net present value of investment represented by
pf (I) + (1 − p)λI − IRB. (9)
This simply represents the probability weighted investment proceeds for either state minus the repayment to the long-term bond-holders in time 2.
Then, the second component takes into account that short-term nancing is at rst sight cheaper than long-term nancing (RM < RB) and thus increases expected bene t by
mI(RB− RM). (10)
This term describes restructuring of the banks' liabilities in the way that banks reduce the issuance of long-term debt by one unit, saving miRB of cost, and increase the issuance of short-term debt, thereby incurring costs of mIRM. The dierence between both is the net gain of extending their maturity transformation by creating
more money.
Thirdly, money creation that replaces long-term nancing entails costs for banks because they are aware of the probability of a bad state in which they have to sale some of their assets in order to service short-term debt holders. The costs are
(1 − p)zmIRM. (11)
Let z = 1/k−1 be the net rate of return for the resold assets, then with probability pbanks have to service not only the debt amount of mIRM, but also a mark-up of z. The crucial element in this optimization problem is that banks do not take into account the incremental aect of money creation on the re sale discount as equation (6) shows. Rather the net return z is assumed to be a constant and independent of the level of money creation. Finally, recalling equation (5) the banks' money creation is bounded by the collateral constraint and therefore constraints the range of expected pro ts. In summary the problem can be written as
max
m,I [pf (I) + (1 − p)λI − IR
B] + mI(RB− RM) − (1 − p)zmIRM (12)
s.t. m ≤ kλ
RM. (13)
Denoting ηthe shadow-value of the constraint, the corresponding Lagrangian for a rep-resentative bank's optimization hence is
LB= (m, I) = [pf (I)+(1−p)λI −IRB]+mI(RB−RM)−(1−p)zmIRM−η(m− kλ RM).
(14) The rst order conditions are
∂LB ∂m = I(R B− RM) − (1 − p)zIRM − η = 0, (15) ∂LB ∂I = pf 0 (I) + (1 − p)λ − RB+ m(RB− RM) − (1 − p)zmRM = 0 (16) and the collateral constraint
m ≤ kλ
RM. (17)
These rst order conditions suggest two solutions, namely an interior and a corner solution. The interior solution implies that banks nance less than a fraction mmax of their investment with money creation. Such a situation is described by a region in
which the shadow-value assumes the value 0 and hence is non-binding. This only occurs if from (15)
RB− RM = (1 − p)zRM. (18)
If the spread in the short-term and long-term interest rate and hence the marginal bene t from borrowing 1 extra unit of short-term debt while giving up 1 unit of long-term debt equals the expected additional cost (including the mark-up z), then m < mmax. Intuitively, a bank's choice of investment and capital structure are independent of each other. It can even be shown that they invest the same amount I as if they had exclusively con ned themselves to pure long-term nancing. In particular, merging (15) and (16) gives the key equation
pf0(I) + (1 − p)λ − RB = −ηm
I . (19)
Taking into account that η = 0, (19) reduces to
pf0(I) + (1 − p)λ − RB = 0, (20)
which is just the rst order condition for the pro t maximization under pure long-term liabilities given by (7) . Clearly, investment and capital structure decisions are decoupled from each other. Finally (20) shows that the bank indeed optimizes if one recognizes that it re ects the rtst order condition absent any short-term deposit is-suance m: The marginal productivity of investment is 0 and thus banks exploit all margins from investments. This is in line with the conclusion that money creation is eventually only restricted by investments, which act as collateral for further money creation. Yet when the spread between both real rates is su ciently big, such that
RB− RM > (1 − p)zRM (21)
is satis ed, then η 6= 0, indicating that the banks operate at a corner solution where m = mmax and (15) is strictly satis ed with inequality. As (17) points out, the op-timal choice of capital structure now depends on the choice of investment. If a bank desires to create more money, it can do so only by increasing the amount of invest-ment since they serve as collateral to back up the promise of riskless short-term debt. In solving the decision variables in terms of parameters, the functional forms for the respective investment project returns need to be speci ed. For both, time 0 and time 1 projects, the return pattern follows a concave function. More precisely, time 0 projects
in the good state are given by
f (I) = ψlog(I) + I. (22)
Note that the banks project in a good state has a return that is strictly greater than 1, that is, any one unit of investment done yields
f0(I) = ψ
I + 1 > 1 > 0. (23)
of marginal revenue in the good state. This is required for the bank to invest some amount I∗ > 0 and hence that some business activity is ensured. Furthermore such projects display diminishing marginal returns, hence the bank's marginal payo falls as I becomes larger:
f00(I) = −ψ
I2 < 0. (24)
Note that the expected return in the good state of a marginal unit of investment is in nite, as lim
I7−→0f
0(I) = ∞. Hence this insures that choosing I∗ > 0 is an optimum for the bank.
Second, time-1 projects adhere to the functional form
g(K) = θlog(K) (25)
for some W − M = K ≤ W . The marginal return of such new late-arriving projects is g0(K) = θ
K > 0. (26)
Also this function displays diminishing marginal returns: g00(K) = − θ
K2 < 0 (27)
This non-stochastic functional form implies that the pro t can be negative, yielding an output that is smaller than the input when θ is su ciently small. However within the context of the model, the parameter θ will be such that the investment proceeds remain positive.
In the case of an interior solution, the bank chooses
I∗ = pψ
m∗ = R B− (1 − p)λ − p pψRM [W − θ(1 − p)RM RB− RM + (1 − p)RM, (29) M∗ = m ∗ I ∗ RM = W −θ(1 − p)R M RB− pRM (30)
which produces a net rate of return on re-sold assets of z∗ = 1 − k
k =
RB− pRM
(1 − p)RM. (31)
(20) clearly shows that in the region where the interest spread is su ciently small, investment decisions is decoupled of spreads only the long-term rate enters the equation. In contrast to this, money creation is represented by (30) is sensitive to interest rate spreads in that it increases for a given level of RB as the gap between both rates widens. Furthermore (31) shows that the net return on re sales is also sensitive to spread dynamics. Holding the long-term rate constant, an increase in the short-term rate lowers z if an interior solution is achieved, because from (31) ∂z∗
∂RM < 0. Intuitively a smaller spread reduces a bank's engagement in money creation and therefore lowers the amount of assets that would be sold in an adverse state of the economy, which in turn by (31) puts less pressure on the discount price k. Finally the total amount of money created, M, decreases in spread decreases for a given level of the long-term rate, because from (30) M∗
∂RM < 0.
When the bank nds itself at a corner solution where m = mmax, then I∗ = −Ω0+p(Ω0) 2− 4λ(p − RB)pψθ 2λ(p − RB) , (32) m∗ = λW RM θ − Ω0− √ (Ω0)2−4λ(p−RB)pψθ 2(p−RB) and (33) M∗ = m∗I∗RM = W [Ω0 +p(Ω0) 2− 4λ(p − RB)pψθ 2θ(p − RB− [Ω0 +p(Ω 0)2− 4λ(p − RB)pψθ]) , (34) and z∗ = λ m ∗ RM − 1, (35) where Ω0 = p(ψλ + θ − λW ) − RBθ + RB RMλW.
The interpretation of (32) − (35) is somewhat analogous to the interpretation for (28)-(31). The only exception is given by the optimal amount of investment. Unlike in the interior solution, the choice of investment is increasing in RM for a given RB at the corner solution, since investment and nancing choices are not decoupled anymore. c) Social optimum
Opposed to banks, the social planer realizes the incremental eect the choice of short-term nancing has on the discount value of the re sales. Moreover he wants to max-imize the households' utilities rather than the banks' pro ts. Since the consumption of households as of time 0 is the dierence between its initial endowment and their investment with banks and patient investors, time 0 consumption is Y − W − I. And since all proceeds nally accrue to the households, consumption derived from invest-ments in these projects as of time 2 is p[f(I) + g(W )] + (1 − p)[λI + g(W − M) + M]. Adding monetary services20 that provide additional consumption in time 2, then the social planer maximizes
U = Y RB−IRB−W RB+p[f (I)+g(W )]+(1−p)[λI +g(W −M )+M ]+M R
B− RM RM (36) s.t. m ≤ kλ RM. (37)
The corresponding Lagrangian is
LP = p[f (I)+g(W )]+(1−p)[λI+g(W −M )+M ]−IRB−W RB+mI(RB−RM)−ηP(m− kλ RM), (38) where ηP is the shadow value of the collateral constraint. Optimizing with respect to m and I gives ∂LP ∂m = I(R B− RM ) − (1 − p)zIRM − ηP(1 − g”(W − M ) (g0(W − M ))2λI) = 0 (39) and ∂LP ∂I = pf 0 (I)+(1−p)λ−RB+m(RB−RM)−(1−p)zmRM+ηP g”(W − M ) (g0(W − M ))2λm = 0. (40) 20See Appendix 1. for a full derivation of the welfare function
Compared to the private solution given by (15)and (16), two ndings stick out. First, for values that satisfy
RB− RM = (1 − p)zRM, (41)
the shadow value of the collateral constraint becomes 0, indicating again an interior solution. In fact, for ηP 6= 0, (35) is identical with (15) , and (36) with (16) . This suggests a striking result: For su ciently little interest rate spreads (between the short-term and long-short-term rate), both the private and social optimum coincide. This is because the marginal bene t of issuing short-term debt is smaller that the expected marginal cost in the form of losses through re sales in the bad state. The choice of investment and money creation is once again decoupled from each other. However if the spread is su ciently high, that is if
RB− RM > (1 − p)zRM, (42)
then ηP 6= 0and the collateral constraint is binding. A more striking result tackles the optimal choice of investment. Rearranging (36) to become
pf0(I) + (1 − p)λ − RB+ m(RB− RM) − (1 − p)zmRM = −ηP g”(W − M )
(g0(W − M ))2 (43) shows that marginal productivity of investments on the left hand side is no longer equal to 0. Since g(W − M) is a concave function, the term on the right hand side turns out to be positive, indicating a positive marginal productivity of investment. Hence in the social optimum banks invest less than privately optimal. Recalling that at the corner solution m can only increase if the collateral I increases, it can be inferred that total money creation in the social optimum is thus less than in the private optimum. Solving in terms of the parameters of the model, the social planer picks for I
21 ISP∗ = −(W λ 2pψ − RBRMθ2Φ2 1− W λ2θ + W λ2pθ + (RM)2pθ2Φ21+ RMλθ2Φ1− RMλpθ2Φ1− RMW λpθΦ1 (W λ3− RBW λ2+ W λ2p − W λ3p) (44)
21Note that these illustrations are taken from Matlab through symbolic manipulation, while all other
calcu-lations have been manually solved. Also I refrain from adding the equation of the optimal M and z in terms of parameters as it would not contribute any further to this work.
where : Φ1 = Φ2+ Φ8 3(RB(RM)2θ2− (RM)3pθ2) + Φ3 Φ2 Φ2= (((Φ6+ Φ5+ Φ4)2− Φ33)1/2+ Φ6+ Φ5+ Φ4)1/3 Φ3 = Φ7 3(RB(RM)2θ2− (RM)3pθ2)+ Φ28 9(RB(RM)2θ2− (RM)3pθ2)2 Φ4 = Φ8Φ7 6RB(RM)2θ2− (RM)3pθ2 Φ5= W2λ3− RBW2λ2+ W2λ2p − W2λ3p 2(RB(RM)2θ2− (RM)3pθ2) Φ6 = Φ38 27(RB(RM)2θ2− (RM)3pθ2)3 Φ7= RBRMW λθ − 2RMW λ2θ − RMW λpθ + RMW λ2pψ + 2RMW λ2pθ Φ8 = (RM)2λθ2− (RM)2λpθ2+ RBRMW λθ − (RM)2W }λpθ and for m m∗SP = Λ1+ Λ5 3(−pθ2(RM)3+ RBθ2(RM)2) + Λ2 Λ1 (45) , where Λ1 = = Λ35 27(−pθ2(RM)3+ RBθ2(RM)2)3 + Λ4+ Λ3 2 − Λ32 !1/2 + Λ 3 5 27(−pθ2(RM)3+ RBθ2(RM)2)3 + Λ4+ Λ3 1/3 Λ2 = (RBRMW λθ − 2RMW λ2θ − RMW λpθ + RMW λ2pψ + 2RMW λ2pθ) 3(−pθ2(RM)3+ RBθ2(RM)2) + Λ25 (−pθ2(RM)3+ RBθ2(RM)2)2 Λ3= (Λ5(RBRMW λθ − 2RMW λ2θ − RMW λpθ + RMW λ2pψ + 2RMW Λ2pθ) 6(−pθ2(RM)3+ RBθ2(RM)2)2
Λ4=
W2λ2− RBW2λ2+ W2λ2p − W2λ3p
2(−pθ2(RM)3+ RBθ2(RM)2)
Λ5= (RM)2λθ2− (RM)2λpθ2+ RBRMW λθ − (RM)2W λpθ
4. Externality and welfare analysis in the Euro area
In order to determine the predicted loss in welfare I adhere to the parameters from both sources, the academic literature and the real world.22 In particular S2011 oers a set of parameters that to some extent need to be modi ed to re ect the features of the Euro area. A brief discussion of how to match the periods from the model with the real-world will prelude this subsection because coming clear on this issue is crucial for the choice of real rates. Then the determination of the interest rate spread will be the major focus. Two courses of actions occur hereby: On the one hand, the spread between the risky and riskless real rate can be derived by using proxies of these rates and then calculating by the dierence to obtain the market risk premia. On the other hand one can approximate the interest rate spread by using a suitable market risk premium. (a) Con nement of the periods
The di culty of the model lies in the determination of the scope of time in particularly because the dierence between RB and RM is determined through preferences in the money-utility-function. It features three periods, a short-term and a long-term in-terest rate. The choice and break up of the periods will be crucial for the choice of the parameters. Two features of the model however suggest to seperate the model into two real periods. First, the household consumes only in two periods, namely t = 0 and t = 2. It is straightforward to interpret the periods in which consumption is done as the main periods. Furthermore period t = 1 is an intermediate period in which housheholds are assumed to hold any proceeds from short-term assets (i.e. money) in the interim until the next consumption period (t = 2) arrives. Second, the interest rates and their role in the model are not characterized by their maturity in rst place, but by their riskiness. The maturity levels of the rates in this model are a necessary result for them 22To the best of my knowledge this model has not been calibrated, so academic literature explicitly refers to
to be risk-free and risky, respectively. 23Hence my pick of the real risk-free and risky rates from the real world does not depend on a match with respect to maturities, but according to their potential to serve as a market-wide ackowldeged risk-free and risky rate, respectively.24Therefore for this analysis I will assume that one year in the real world will correspond to a consumption period in the model. More precisely, I will de ne the rst period (t = 0) to be the year of 2011, the second period (t = 2) to be the year 2012.25
(b) Real risk-free and risky rates
At the end, the model's prediction and implication break down to nding the best proxy for the risky and riskless real interest rate. Of course the scope of potential candidates in the Euro area encompasses more than one real-world rate as a candidate. Therefore it is worth discussing brie y the course of action of this paper with respect to nding a proper proxy. I restrict the proxy candidates to two for each rate, thereby oering scenarios.
i) Real risk-free rate
The yield from 10 year-BUNDs: The Model characterizes RM as a real, riskless, and short-term rate. In the light of the latter two characteristics, the top rated sovereign bonds in the Euro area such as the German BUND are input candidates. In contrast to (but not limited to) US-based research, no clear equivalent counterpart for the 10-year T-Bills in the role of a risk-free rate exists in Europe. Unlike the US, the Euro area member states are not able to secure the risklessness of their debt, since the independence of the European Central Bank prevents monetisation of sovereign debt by printing money and paying outstanding debt o. Therefore even in the best riskless sovereign debt security, there will be some remaining risk of default. The usual work around is to substracting the price of a credit default swap, which eventually leads to a rate that can be considered riskless. Thus for t = 0, i.e. for the year 2011, I collected daily data on 10-year German sovereign bond yield and took the average so as to account for seasonalities.
23Recall that the signal of the state of the economy in t = 1 eventually makes the long-term debt risky while
the short-term rate stays risk-free.
24For example I would consider a 10-year risk-free sovereign bond and a risky rate on the basis of a 1-year
average dividend yield of a stock index as potential parameter candidates.
25Since the year 2013 has not ended yet, incorporating this year would not be properly in terms of a
Figure1.1: Average yield of 10-year BUNDS
Source: Deutsche Bundesbank for the BUND yield, Datastream for the CDS Spread
The implicit yield of the German 10-year sovereign bond over the year 2011 oscillates between 1.87% and 3.37%, as Figure 1.1 displays26. The corresponding CDS spread for German sovereign debt with a maturity of 10 years quotes at 56 basis points. This way I calculated the nominal risk-free rate of return and then took the average to obtain the averaged nominal risk-free rate of return, quoting at a growth rate of 2.10%. Then I generated the real risk-free rate of return by substracting the harmonised index of consumer prices, the common measure of in ation for the Euro area. By averaging the result, i.e. the real risk-free rate, I obtained the average real risk-free rate.
Figure1.2: Average yield of 10-year BUNDS
Source: Deutsche Bundesbank for the BUND yield,
Eurostat for theHICP
Figure 1.2 displays the path of the real risk-free rate. Substracting the monthly averages fo the HICP from the monthly averages of the risk-free rate yields the real risk-free rate, which oscillates between -1.69% and 0.26%. Given the large degree of uncertainty in the sovereign bond market in the Euro area at this time, investors re-frained from storing their money in bonds other than the German BUND, thereby increasing demand and pushing down the BUND-yield . average real risk-free rate is estimated to be -0.6%.27
Euro area yield curve:
Yet for this analysis I will also make use of the Euro area yield curve, a ctive rate that is constructed by the European Central Bank and that measures the average yields of a weighted portfolio of bonds issued by Euro area member states. Such a weighted rate of return seems to be riskier than a top-rated sovereign bond yield like the return from the German BUND, since the latter establishes a lower bound of the weighted return as it is considered the safest bond in the Euro area. Yet the weighted average is based on a pool of debtors and thus represents the yield of a diversi ed portfolio of sovereign bonds. Real time data on German BUNDS and calculations undertaken by the ECB indicate however that the Euro area yield is still calculated to be riskier.As Figure 2.1 shows, the 10-year Euro area yield curve remains fairly stable between 2.50% and 3.65%. The credit default spread is derived from the 10-year credit default spread of sovereign debt from Eurozone members. For the year 2011, the Eurozone CDS averages 166 basis points. Substracting the credit default spread index for the Euro area yields a in nominal terms denoted risk-free rate that follows the same path as in the case for the 10-year BUND, yet drops more sharply in summer 2011. This sharp drop leads to an averaged rate that is projected to be lower by 50 basis points in comparision with the BUND-based rate.
27Note that this implies RM = 0.994and hence from the calculations in Appandix 1, RM = 1/(β + γ) > 0
is still satis ed: Assuming that β is less than 1, 0 < RM
Figure 2.1: 10y Euro area yield, CDS-Spread, Euro area risk-free rate and Average Euro area risk-free rate
Source: ftalphaville.ft.com for the Euro area CDS-Spread , ECB for the 10-year Euro area yield
Given the increase in the CDS spread, the average risk-free rate for the year 2011 amounts to 1.55%. Figure 2.2 shows the nominal risk-free rate, the HICP and real and average real risk-free rate. The real risk-free rate follows somewhat the same pattern as the real rate on the grounds of the BUND yield. The sharper drop (than in the BUND-based rate) starting in spring seems to indicate the dierent risk-pro le between both rates. While the German sovereign debt is considered fairly risk-free, the ctive Euro area yield entails a higher degree of risk since it contains risky candidates such as Greece, Spain or Portugal. Hence the average real risk-free rate settles at -1.21%.
Figure 2.2: Euro area yield curve, HICP, Euro area risk-free and average risk-free rate
source: ECB for the Euro area yield, Eurostat for theHICP
At this point it is worth pointing out the interpretation of such a negative interest rate. The elevated risk-pro le of the Euro area yield curve implies that investors with large stocks of investment capital are willing to accept a lower interest rate in return as long as they can store their capital somewhere. Hence in a riskier environment (as re ected by a low Euroarea-yield-based average real risk-free interest rate) investors are willing to even pay for the possibility of storing their capital. Consequently the real risk-free rate is expected to be on lower levels than in a less risky environment.
ii. Real risky rate
It appears to be far more di cult to approximate the risky rate of return. Unfortunately S2011 has not made a clear distinction in this matter. Sticking to the model, one could calculate the average rate of long term deposits such as (non-checkable) savings accounts and time accounts as well as corporate bonds issued by European banks. However the di culty of collecting aggregate and average data on especially bank bond yields calls for a dierent approach. Therefore as highlighted above I will draw on real-world data of market risk premia and equity risk premia that commonly represent the mark-up on a risk-free asset. In particular, since no aggregate or average data for the Euro area is given, I take the average of these rates and add it to the BUND-yield and Euro area yield curve, respectively.
Equity Risk Premium: STOXX-50-dividend-yield-spread: Often analysts cal-culate the average dividend yield of the STOXX 50 and substract the best candidate for a risk-free rate such as the BUND from it in order to obtain a representative equity risk premium for the Euro area. This in turn indicates that the European stock index commonly serves as a proxy for the risky interest rate. The anual average dividend of 2011 of the blue chip rms listed at the STOXX 50 amounts to 3.53%28. From the upper section we know that the 10-year BUND gives a nominal risk-free rate of 2.10% Substracting the sovereign bond yield from the average dividend yield implies a market equity premium of 1.43%. The risky nominal rate becomes RB = 1.0353 using the 10-year BUND as the risk-free rate. Analogously in the case of the Euro area yield, on the grounds of a nominal risky rate of RB = 1.0353 the market equity premium becomes 2.04%.
Market risk premium: A second approach suggests to use calculations (others than just described) of market equity risk premium from nancial institutions and market participants engaged in business valuation. A breakdown of applied market risk premia in the Euro area was collected and re ned in an IESE-survey by Fernández, Aguir-reamaolla and Corres (2011). On the grounds of their survey, I found that the (un-weighted) average market risk premia in the Eurozone amounted to 5.98%. In countries with macroeconomic importance such as Germany, France and Italy plus Netherlands, the median value is between 5% and 6% and follows a disbtribution with a mean of approximately 5.5%-6% and a std. deviation ranging from 1.4%-1.6%. Moreover these premiums follow a distribution that seems to be similarly shaped accross member states of the Euro area29 . Such a nding not only provides evidence on an existent nancial market integration, but supports that the applied averaged market risk premium has potential to be representitive for all Euro area member states.30
The results from the survey then imply a nominal risky interest rate of RB = 1.0808 and RB = 1.0747 when the riskless rate is the BUND and the Euro area 10-year yield curve respectively.
All nominal yields are summarized in table 1. Not that subsequently the term assumption will refer to the four underlying scenarios that each feature a dierent set of RM − RB-combinations.
RMnominal/RBnominal 10-year BUND 10-year Euro area yield STOXX 50 2.10%/3.53%(Assumption 1) 1.49%/3.53% (Assumption 3) IESE Survey 2.10%/8.08%(Assumption 2) 1.49%/7.47% (Assumption 4)
:Table 1: Matrix with nominal risk-free and risky rates
Interestingly both the STOXX 50 and IESE survey estimates produce completely dierent risk-premia. While the rst one estimates the average risk-premia accross assumption 1 and 3 to be a mere 173 basis points, the survey estimates it to be 598 basis points. There is a dierence in 425 basis points. The explanation is straightforward: the Euro STOXX contains some of the largest rms by capitalization, that are big enough and both geographically and business-wise diversi ed enough to cushion uctuations and deal with risks. The risk that is priced in Euro STOXX 50 companies' dividends is the equity risk, hence the mark-up underlying assumption 1 and 3 is the equity risk 29See table A.2 in appendix 2 for a detailled list of Euro area members. No data was available for Cypress,
Estonia, Malta, Slovakia and Slovenia.
30If market risk premia were heavily dispersed, any choice would clearly not be representative for the Euro
premium. In contrast the IESE survey investigate the market participants' mark-up in a country's market, hence it calculates the market risk premium. Therefore assumption 2 and 4 work with a signi cantly higher risk-premium, indicating that the market as a whole was perceived to carry larger risk-positions.
Sofar I have calculated the nominal average rates. To get the real rates, the Fisher equation implies substracting the average HICP for the year 2011 (2.70%), which yields the real risk-free and risky rate, as listed in Table 2.31Table 2 summarizes the real rates of return:
RMReal/RBReal 10-year BUND 10-year Euro area yield
STOXX 50 −0.60%/3.53% (Assumption 1) −1.21%/3.53% (Assumption 3)
IESE Survey −0.60%/5.38% (Assumption 2) −1.21%/4.77% (Assumption 4)
Table 2: Matrix of real risk-free and risky rate
Although the funding in the model stems exclusively from households, I consider any representation through real world rates appropriate, as long as geographical equivalence of the variables in order to share the same risk-pro le is given. The non-existence of a government acting as an agent therefore supports this course of action since no explicit distinction between the composition and origin of the rate determination is required.32 Last but not least the BUND and the Euro area yield curve are realistic approxima-tions as they re ect the price of such large debt and money transacapproxima-tions that are capable of servicing the large demands from banks. In fact banks are an important demand component when German BUNDs are placed in the market and potentially were if
Eu-robonds were to be issued.
(c) Parameters
The baseline scenario in S2011 uses for the real rates RM = 1.01 and RB = 1.04, and for the parameters of the model θ = 150, ψ = 3.5, p = 0.98, λ = 1 and W = 140. 33
These parameters were applied by S2011 and re ect the features of an adavanced economy in a developped country, in particular in the US34. In order to provide a common ground for comparability and discussion between my and S2011's replication, 31http://www.global-rates.com/economic-indicators/in ation/consumer-prices/hicp/Euro area.aspx as of
july 18th 2013
32If the government were to play a role in this model, using real world sovereign bonds to proxy the riskless
late in this model might give rise to consistency and hence validity disputes.
33Note that the parameter for the initial wealth of the household, Y, is not needed at this point as it does
not enter the rst order coniditions.
