Master thesis Finance

1

On retirement wealth and income via glide paths and portfolio insurance strategies

Master thesis Finance

Abstract

The purpose of this paper is to provide a broader perspective on retirement investment plans by considering the traditional glidepath, the inverse glidepath, and portfolio insurance strategies covering a worldwide sample of country indices over 116 years. By analyzing data from stock and bond markets for the period 1900 to 2015, we present three main results. First, we show that the inverse glidepath and constant mix strategy usually outperforms the traditional classic glidepath. Second, we show that the CPPI usually outperforms the TIPP. The TIPP happened to be less aggressive in scenarios where the stock market went up considerably. Third, we find different results for the period 1991-2015, since in this period the bond market outperformed the stock market from 2000-2015. For this period, the traditional glidepath and TIPP would have outperformed strategies that are fully invested in stocks.

Studentnr: s2496992

Name: Edwin van der Nol

Study Program: Master of Science (MSc.) Finance Supervisor: Prof. Dr. T.K. Dijkstra

Field Key Words: Retirement investment strategies, insurance policy, wealth, risk

JEL codes: G11

2

1. Introduction

The standard advice from financial advisors for investing for retirement is to invest in stocks when you are young and to gradually move into bonds when you get older. The argument is basically that young people have lots of time to recoup losses and are able to take larger risks. People close to retirement have more to lose and less time to recover from bear markets. They want greater certainty that the amount of money they anticipate to need in retirement will be available and therefore take less risk the closer they get to retirement. The financial advisors have two primary responsibilities concerning retirement investment plans. The first is to maximize the real value of retirement wealth and the second is to minimize uncertainty around the prospective retirement spending (Arnott, Katrina, Sherrerd, and Wu, 2013). Studies by Shiller (2005), Estrada (2014), Basu and Drew (2009) suggest that the standard advice from financial advisors is too conservative to achieve these responsibilities.

In this paper we compare three retirement investment strategies, one traditional and two alternatives, with respect to their ability to maximize the real value of retirement savings and to minimize the uncertainty around the prospective retirement date. The traditional strategy is the classic glidepath, moving from equity-centric to bond-centric investing as we age, the standard advice by financial advisors. This advice is followed widely as reflected in the size and growth of so-called target-date funds. The second (alternative) strategy is the inverse glidepath, the opposite of the classic glidepath strategy. The third (alternative) strategy is the constant mix strategy that keeps a constant 50-50 stock-bond allocation. All three strategies are obtained from the paper by Estrada (2014).We expand on Estrada (2014) by investigating a different time period and a different length of working life. In this paper we investigate the period 1900 to 2015 and a working life of 42 years. We also go beyond Estrada (2014) by investigating whether strategies that explicitly aim to insure the value of the investments at retirement will improve the results for retirement. We look into two well-known insurance strategies: the “constant proportion portfolio insurance” strategy (CPPI) and the “time invariant portfolio protection” strategy (TIPP). The CPPI is obtained from the paper by Perold and Sharpe (1995) and the TIPP is obtained from the paper by Estep (1988). Both strategies are insurance policies if there is a substantial ‘floor’, otherwise it is just a constant mix strategy.

Our main research question is the following:

3 The sub-questions to be answered in this study are:

1. How well did the strategies do in the past? In particular, what are the historical values of the mean, median, lowest and highest values, standard deviations, average of the lowest decile and quartile and average of the highest decile and quartile of each strategy? We answer this by analyzing the outcomes by terminal wealth over 116 years and not by analyzing the value of the portfolio during the 42-year holding period.

2. What are the differences between the historical values of each strategy over time? We answer this by analyzing the outcomes over three time periods. The three time periods are from 1900-1965, 1966-1990, and 1991-2015.

This paper is described from the perspective of a US investor. We focus on the US pension market. It is one of the largest markets in the world. For a proper understanding the reader ought to know that the US income for retirement is built on three ‘pillars’ (Moore, 2011). The first pillar is a government pension (social security), the second pillar is the employer’s pension, and the third pillar if any is an additional pension. This paper is relevant in particular for the third pillar, an individual retirement plan (additional pension). The age of retirement in the US is not fixed, but there are a few ages that are significant for retirement purposes. In this paper the age of retirement in the US is fixed at 67 years, because this is the retirement age for social security purposes for those born after 1954.

The paper is organized as follows. In the next section we discuss the literature related to the retirement investment strategies from the paper by Estrada (2013) and the strategies that aim to insure the value of the investments at retirement, the CPPI and TIPP strategies. Furthermore, we present the empirical results of the existing literature for these retirement investment strategies. Section 3 will present an overview of the data. Section 4 will present the methodology for implementing the retirement investment strategies and how to measure the results. We discuss our results in Section 5. Finally, Section 6 will present the conclusions.

2. Literature overview

4 not a function of the number of years to retirement. They depend on the so-called multiplier, the portfolio value and a ‘floor’. These terms are explained in more detail later in this section and in the methodology.

Shiller (2005) was the first to emphasize that investors following a traditional glidepath strategy have a large exposure to stocks when they are young and their savings are low and a small exposure to stocks when they are older and their savings are higher. Shiller (2005) finds that the glidepath strategy is generally too conservative. It will not maximize the real value of retirement wealth and minimize uncertainty around the prospective retirement spending that will be available. In the early years the classic glidepath portfolio would perform well in the stock market only for a relatively small amount of money and would pull most of the portfolio value out of the stock market in the latest years when earnings are the highest. Shiller (2005) argues that a classic glidepath will usually underperform portfolios fully invested in stocks.

Basu and Drew (2009) find that investors should become more, rather than less aggressive over time. They consider several classic glidepath strategies and their opposites. Basu and Drew (2009) find that inverse glidepath strategies which, invest in bonds when you are young and move into stocks when you get older, produce far superior wealth outcomes relative to traditional glidepath strategies. Basu and Drew (2009) show that by investing conservatively in the middle and later years of investor’s investment horizon, the classic glidepath strategies work against the investor’s investment objectives. Their results support those of Shiller (2005) and suggest that investors should follow the classic glidepath opposite to those featured by target-date funds.

5 terminal wealth but also have a higher volatility. Volatility is viewed as a measure of risk, but is two-sided. The volatility is perhaps better seen as a measure of the uncertainty about terminal wealth. Investors should and do also care about their performance in worst-case scenarios (low-return scenarios). The minimum terminal wealth of inverse glidepath strategies in all scenarios is higher than with their classic glidepath strategies. These results imply that although classic glidepath strategies keep investors less uncertain about their terminal wealth than inverse glidepath strategies, they do not necessarily provide them with a higher terminal wealth at retirement in worst-case scenarios.

6 The CPPI and TIPP are dynamic asset allocation strategies where the allocation depends on the development of the portfolio value through time and the desired level of protection. Their portfolio insurance character is usually most clear when the strategies are ‘convex’, meaning essentially that they buy after a rise of the stock market, and sell after a fall. They are expected to do well in rising markets, and offer protection in bear markets. See Perold and Sharpe (1995) for extensive elaborations. Other strategies that fit in principle into this framework are buy&hold and constant mix, but these are not really portfolio insurance strategies. According to Basu, Byrne and Drew (2011), the dynamic switching strategy produces superior returns for most investors compared to classic glidepaths that are based solely on age or target retirement date.The constant mix strategy can be seen as a combination between the classic glidepath and the inverse glidepath. In this paper we will compare this strategy with the classic glidepath, the inverse glidepath, and the portfolio insurance versions of TIPP and CPPI. The constant mix is a ‘concave’ strategy in which stocks are bought after a fall, and sold after a rise in order to keep the proportion invested in stocks the same. It typically does well in markets that ‘move sideways’, for example which are volatile and mean reverting. See Perold and Sharpe (1995) for discussions. Many pension funds follow this strategy. Here we take a constant mix of 50% stocks and 50% bonds.

7 decline below a pre-set floor (or there is a negative bond return). Second, the floor is adjusted continuously to be a specified percentage of the highest value the portfolio reaches. Third, protection is continuous and has no ending date. Fourth, computations are simple and can be made at essentially no cost (no computer, no Black-Scholes formula, and no estimates of standard deviation). Fifth, the results of this strategy are more sensible than put replication, because they imply an attitude toward risk that varies smoothly with wealth and is not affected by time. Sixth, there is less trading, which means that the cost of equivalent protection is lower. These characteristics also apply to CPPI, excluding characteristic two because the CPPI used a fixed floor.

The CPPI and TIPP are trading strategies that allows an investor to maintain an exposure to the upside potential of stocks (risky asset) while providing a capital guarantee against downside risk. The outcome of the CPPI and TIPP are somewhat similar to that of buying an option, but does not use option contacts. Estep and Kritzman (1988) compare TIPP with a put replication and the CPPI. They suggest that put replication is deficient primarily because it is dependent upon a specific time horizon, typically one year. Put replication provides protection that is indexed only to the initial value of the portfolio. Subsequent gains in the portfolio are not protected. Estep and Kritzman (1998) suggest that CPPI gained immediate acceptance as an alternative to put replication. An obvious advantage is its simplicity. There is no need to alter the portfolio’s mix abruptly at an arbitrary date. The asset mix changes only as a function of the portfolio’s value and not as a function on the passage of time. This asset mix usually reduces trading and associated costs. These characteristics are similar to the TIPP, as mentioned above. A disadvantage of the CPPI is (like put replication), if the portfolio’s value rises faster than the floor, after a while there is no meaningful protection. This protection is an essential difference with the TIPP, because TIPP is less aggressive in scenarios where the stock market went up considerably. By increasing the floor in good times, the allocation to stock diminishes considerably. Additional, Estep and Kritzman (1988) suggest that the TIPP is CPPI with a different and better rule for setting the floor.

3. Data

8 2016. Dimson, March, and Staunton (2002) use for equity a total average return per decennia of total yearly returns. For MSCI, we use total yearly returns. Dimson, March, and Staunton (2002) set out the total average returns per decennia of worldwide investment in sixteen-country world equity indexes and bond markets from the perspective of a US investor and therefore we focus on the US pension market. The countries are Australia, Belgium, Canada, Denmark, France, Germany, Ireland, Italy, Japan, The Netherlands, South Africa, Spain, Sweden, Switzerland (equity data from 1911), United Kingdom and United States. The home currency is US dollars, and the inflation rate is as for the United States. The short-term risk-free rate is taken as the return on US treasury bills. The US treasury bills for this paper are calculated as average from the period 1900 to 2015. The world equity series calculated by Dimson, March, and Staunton (2002) comprise a common currency world index. For each period, they take a market’s local-currency return and convert it to US dollars. They therefore have the return that would have been received by a US citizen who bought foreign currency at the start of the period, invested it in the foreign market throughout the period, liquidated his or her position, and converted the proceeds back at the end of the period into US dollars. Dimson, March, and Staunton (2002) assume that at the beginning of each period the investor bought a portfolio of sixteen such positions in each of the countries covered in this study, weighting each country by its size. They use GDP weights with start-decade rebalancing before 1968 due to a lack of reliable data on capitalizations prior to that date. Thereafter, they use country capitalizations taken from MSCI. We used the MSCI for the equity data for total yearly returns worldwide from 1970 until 2016. The sixteen-country world bond market index follows the same principles. It is weighted by country size, to avoid giving, say, Belgium the same weight as the United States. Equity capitalization weights are inappropriate here, so the bond index is GDP-weighted throughout. The global database of Dimson, March, and Staunton (2002) is used in this research for the bond returns for the period 1900 to 2000. The average of US 15-year bond returns and Germany 15-year bond returns are used for the missing data of 2001 to 2015.

9

4. Methodology

The literature review shows that the classic glidepath underperform the inverse glidepath and constant mix strategy. The literature review also shows that the (convex) CPPI and TIPP will perform better than the (concave) constant mix strategy. The CPPI and TIPP tend to give good downside protection and to perform well in up markets. These strategies will anticipate to falling and rising markets by switching to bonds during recessions and switching to stocks during periods of high economic growth. Therefore, to examine the effect of the impact of the inverse glidepath, constant mix strategy, CPPI and TIPP on retirement income and wealth we hypothesized the following:

H0: The inverse glidepath, constant mix strategy, CPPI and TIPP have no or negative effect on the real value and uncertainty around the client’s prospective retirement compared to the classic glidepath.

H1: The inverse glidepath, constant mix strategy, CPPI and TIPP have positive effect on the real value and uncertainty around the client’s prospective retirement compared to the classic glidepath.

For the strategies classic glidepath, the inverse glidepath, and the constant mix strategy we used the same approach. The individual person starts on the age of 25 until the age of 67. To determine the investment wealth of the investor at retirement, we assume a consistent real (inflation-adjusted) $1,000 annual contribution over a 42-year career and annual rebalancing and ignoring both taxes and transaction costs. The rebalancing takes place annually, because otherwise this may lead to very high transaction costs as the investor has to buy small amounts of assets very frequently. To determine the retirement wealth, we used hundred and sixteen-years of stock and bond market returns from 1900 until 2016. The first individual person starts working in 1900 and retires at the end of 1941 for the retirement age of 67. The last individual person starts working in 1974 and retires at the end of 2015 for the retirement age of 67. The average allocation for all three strategies is 50/ 50. These strategies are:

1. Classic glidepath: starts with 100% in equity and gradually switches the portfolio into 100% bonds and 0% stocks as the target date approaches.

2. Inverse glidepath: starts with 0% in equity and gradually switches the portfolio into 0% bonds and 100% stocks as the target date approaches.

10 The three strategies follow:

𝑊_𝑡+1= 𝑊_𝑡(1 + 𝑟_𝑝,𝑡+1(𝑥𝑡)) (1)

 Wt+1 = investor’s wealth at the end of the period.

 Wt = investor’s wealth at the beginning of the period.

 Rp,t+1 = the portfolio return. The three strategies have a return on the invested part in stocks and bonds.

 (Xt) = a function of the asset weights chosen at the beginning of the period. The investor’s wealth at the end of the period is calculated according to Ang (2014).

The CPPI and TIPP strategies follow a different approach. In contrast to the classic glidepath, the inverse glidepath and constant mix strategy approach we do not worked with a $1,000 annual contribution. Instead, the CPPI and TIPP strategies start with a present value of $35,090.83. We assume annual rebalancing and ignoring both taxes and transaction costs. The present value is calculated as follows: 𝑃𝑉 = 𝐶0+_(1+𝑟𝐶1 1)+ 𝐶2 (1+𝑟2)2… + 𝐶𝑇 (1+𝑟𝑇)𝑇 (2)

 Ct = the (positive or negative) cash flow at date t. In this equation Ct is $1,000. Where t is the number of periods to the retirement date of the portfolio strategy.

 rt = the risk-free rate. In this paper the risk-free rate is taken as the return on US treasury bills. The US treasury bills are calculated as average from the period 1900 to 2015.

The present value is calculated according to Hiller et al. (2012). The allocation of the strategies is as follows:

1. CPPI: This strategy implies selling stocks in a falling market and buying stocks in a rising market. And a strategy that maintains a fixed floor in the portfolio (not more than 100% stocks or bonds). The value of the portfolio in excess of the floor is the buffer, which is used to cushion risk. The CPPI follows:

E = m × (portfolio value -/- floor) (3)

 E = the exposure to stocks.

 m = a fixed multiplier. The multiplier determines the aggressiveness of the strategy, and is related to the risk attitude of the investor. The strategy can default if the drop in the stock market price exceeds 1/m, implying that the portfolio value falls below the floor.

 Floor = the investor selects a floor below which he does not want the portfolio value to fall.

11 protection against a drop of at most 33.33% before rebalancing the portfolio). Then on the first day, the investor will allocate (3 × ($35,090.83 − $30,000)) = $15,272.49 to stocks and the remaining $19,818.34 to bonds. The exposure to stocks is 43.52% and to bonds 56.48% of the portfolio value. The exposure will be revised as the portfolio value changes. Now suppose that the portfolio value goes up with 2%, so that the portfolio now is worth $35,792.65. The floor is still $30,000. Stocks exposure is (3 × ($35,792.65 − $30,000)) = $17,377.95 and the remaining $18,414.70 to bonds. The exposure to stocks is 48.55% and to bonds 51.44% of the portfolio value. Assume the portfolio value now decline by 1.5%. The portfolio value drops to $35,255.76. The floor stays at $30,000. Stocks holdings now are (3 × ($35,255.76 − $30,000)) = $15,767.28 and the remaining $19,488.48 to bonds. The exposure to stocks is 44.72% and to bonds 55.28% of the portfolio value. The CPPI is calculated according to Perold and Sharpe (1995).

2. TIPP: This strategy addresses the problem of no meaningful protection by continuously adjusting the floor to a specified percentage of the highest value that the portfolio reaches. It is effectively an ‘improved version’ of CPPI, with an algorithm adjusting the floor. The effect is that the extreme high levels of leverage are being prevented. In this paper the client will not more invest than 43.52% in equity and not less than 56.48% in bonds.

12

5. Results

The results of the strategies described in section 4 are presented in this section. For the retirement investment strategies we used a different approach than the insurance policy strategies, therefore we treat these strategies separately. The results of the classic glidepath strategy, the inverse glidepath strategy, and the constant mix strategy are presented and described in Section 5.1. Section 5.2 described the results of the strategies that explicitly aim to insure the value of the investments at retirement (insurance policies), the CPPI and TIPP.

5.1. The traditional and alternative retirement investment strategies

The results for the three retirement investment strategies, classic glidepath strategy, the inverse glidepath strategy, and the constant mix strategy, are discussed below. The performance of the retirement investment strategies for the period from 1900 to 2015 is discussed in Section 5.1.1. Section 5.1.2. described historical values of each strategy over three time periods. The three time periods are from 1900-1965, 1966-1990, and 1991-2015.

5.1.1. Retirement investment strategies for the period from 1900-2015

Table 1. A comparison of the classic glidepath, the inverse glidepath, and constant mix strategy, 1900-2015

13 Glidepath Inverse glidepath Constant mix 100 → 0 0 → 100 50/50

Ending retirement assets (World) pension age of 65 Mean $117,547.55 $135,783.60 $124,932.67 Median $92,844.53 $144,406.32 $97,715.56 Max $265,536.66 $283,484.30 $225,862.27 AvgD10 $223,391.65 $192,765.10 $210,726.17 AvgQ4 $165,728.37 $178,038.85 $175,340.22 SD $69,252.06 $53,459.00 $57,352.66 Min $39,622.02 $49,984.92 $46,845.03 AvgD1 $43,046.97 $54,950.58 $53,841.29 AvgQ1 $53,771.66 $85,580.27 $87,078.13

The results of table 1 show that the traditional classic glidepath allocation does not meet the primary responsibilities concerning retirement investment plans. The classic glidepath strategy results in a lower mean retirement wealth than the inverse glidepath strategy or constant mix strategy, even for the bad-case scenarios. The mean retirement wealth of the inverse glidepath is more than 15.5% higher than the classic glidepath ($135,783.60 versus $117,547.55). The mean retirement wealth of the constant mix strategy is more than 6% higher than the classic glidepath ($124,932.67 versus $117,547.55). The analysis is based on real returns and these are differences in purchasing power.

Furthermore, the classic glidepath strategy and the constant mix strategy have a higher mean retirement wealth than the median retirement wealth. This indicates a positive skewness in the distribution of retirement wealth, which in turn suggests two things. First, it suggests that these distributions have a higher upside potential than downside potential. Second, it implies that the probability of obtaining at least the mean retirement wealth is lower than 50%. In contrast to these strategies, the inverse glidepath strategy shows a higher median retirement wealth than the mean retirement wealth. This suggest that these distribution has a higher downside potential than upside potential and it implies that the probability of obtaining at least the mean retirement wealth is higher than 50%. The median retirement wealth of the inverse glidepath is more than 55% higher than the classic glidepath ($144,406.32 versus $92,844.53). The median retirement wealth of the constant mix strategy is more than 5% higher than the classic glidepath ($97,715.56 versus $92,844.53).

14 highest quartile. The classic glidepath strategy has the highest average retirement wealth in the highest decile.

However, as already mentioned, the goal of traditional classic glidepath is not to maximize expected retirement wealth, but rather to provide an acceptable balance between the risk and return. As table 1 shows, the standard deviation of the inverse glidepath and the constant mix strategy is lower than the classic glidepath strategies. In other words, the classic glidepath strategy keeps investors more uncertain about their retirement wealth than do the inverse glidepath strategy and the constant mix strategy. It is important to notice that the standard deviation considered here measures uncertainty about retirement wealth, not uncertainty about the value of the portfolio during the holding period. Standard deviation is one measure of risk when focusing on saving for retirement. Investors do also care about their performance in low return scenarios. The classic glidepath also underperform the inverse glidepath and the constant mix strategy to give the investors greater confidence about the bad- case scenarios. As table 1 shows, the classic glidepath strategy has a smaller value of the lowest retirement wealth than the inverse glidepath strategy and constant mix strategy. These results imply that the classic glidepath strategy keeps investors more uncertain about their retirement wealth than inverse glidepath strategies and constant mix strategies, and this strategy do not provide the investors with more capital at retirement in worst-case scenarios. The rest of the bad scenario variables are in the same direction. The average retirement wealth in the lowest decile and the average retirement wealth in the lowest quartile are higher for the inverse glidepath strategy and constant mix strategy than the classic glidepath strategy. The average retirement wealth in the lowest decile of the inverse glidepath is more than 27.5% higher than the classic glidepath ($54,950.58 versus $43,046.97). The average retirement wealth in the lowest decile of the constant mix strategy is more than 25% higher than the classic glidepath ($53,841.29 versus $43,046.97). The average retirement wealth in the lowest quartile of the inverse glidepath is more than 59% higher than the classic glidepath ($85,580.27 versus $53,771.66). The average retirement wealth in the lowest quartile of the constant mix strategy is more than 61.5% higher than the classic glidepath ($87,078.13 versus $53,771.66).

5.1.2. Retirement investment strategies over time

15 Table 2. A comparison of the classic glidepath, the inverse glidepath, and constant mix strategy, 1941-1965, 1966-1990, and 1991-2015

This table shows summary statistics for three retirement investment strategies evaluated over three periods. The three time periods are from 1900-1965, 1966-1990, and 1991-2015. The first person retired in 1941, therefore each part consist 25 year working lifetimes. The retirement investment strategies are described as mentioned above in table 1. For each of the three strategies, the statistics describe the series that collects the retirement wealth across three periods of 25 working lifetimes and include the mean, median, lowest (Min) and highest (Max) values, standard deviation (SD), average of the lowest decile (AvgD1) and quartile (AvgQ1) and average of the highest decile (AvgD10) and quartile (AvgQ4).

Glidepath Inverse glidepath Constant mix 100 → 0 0 → 100 50/50 1941-1965 1966-1990 1991-2015 1941-1965 1966-1990 1991-2015 1941-1965 1966-1990 1991-2015

Ending retirement assets (World) pension age of 67

The results of table 2 show that the traditional classic glidepath allocation does not meet the primary responsibilities concerning retirement investment plans for the first two periods, but the classic glidepath strategy shows better results in the third period. For the first two periods, the classic glidepath strategy results in a lower mean retirement wealth than the inverse glidepath strategy and constant mix strategy, even for the extreme bottom tail of the distribution. For the third period, the classic glidepath strategy results in a higher mean retirement wealth than the inverse glidepath strategy and constant mix strategy. The reason for this is that the bonds outperform stocks for the period 2000-2015. This is caused by the “Dotcom bubble” (1999-2000) and the “Global financial crisis” (2007-2008). Therefore, the classic glidepath strategy has a higher mean because this strategy invests more in bonds in the latter years than the inverse glidepath strategy and constant mix strategy.

For the third period, the mean retirement wealth of the classic glidepath is more than 12.5% higher than the inverse glidepath strategy ($201,381.58 versus $178,788.46). The difference between the classic glidepath strategy and the constant mix strategy is much lower. The mean retirement wealth of the classic glidepath strategy is more than 3% higher than the constant mix strategy ($201,381.58 versus $195,491.15).

In the first two periods all three strategies have a higher mean retirement wealth than the median retirement wealth. As above mentioned, a positive skewness in the distribution of retirement wealth suggests that these distributions have a higher upside potential than downside potential and it implies that the probability of obtaining at least the mean retirement wealth is lower than 50%. In contrast to the first two periods, the third period shows the opposite of these results. In the third period the three strategies show a higher median retirement wealth than the mean retirement wealth. This suggest that these distribution has a higher downside potential than upside potential and it implies that the probability of obtaining at least the mean retirement wealth is higher than 50%. The median retirement wealth of the classic glidepath is more than 19% higher than the inverse glidepath ($213,483.75 versus $179,299.68). The median retirement wealth of the classic glidepath is more than 6% higher than the constant mix strategy ($213,483.75 versus $201,070.46). These differences in purchasing power are relevant enough for investors to evaluate carefully.

17 However, it is important to achieve an acceptable balance between risk and return. As table 2 shows, the standard deviation of the inverse glidepath is higher than the classic glidepath strategies for all three periods. In other words, the inverse glidepath keeps investors more uncertain about their retirement wealth than the classic glidepath. The constant mix strategy produced only in the first period a higher standard deviation than the classic glidepath. Besides the standard deviation as measure of risk, investors do also care about their performance in low return scenarios. The classic glidepath fails to give the investors greater confidence about the bad scenarios in the first two periods. As table 2 shows, the lowest retirement wealth is lower with classic glidepath strategy than with the inverse glidepath strategy and constant mix strategy. These results imply that the classic glidepath keeps investors more uncertain about their retirement wealth than the inverse glidepath strategies and constant mix strategies, and they do not provide them with more capital at retirement in worst-case scenarios. The rest of the bad scenario variables are in the same direction for the first two periods. The average retirement wealth in the lowest decile and the average retirement wealth in the lowest quartile are higher under the inverse glidepath strategy and constant mix strategy than the classic glidepath strategy. In contrast to the first two periods, the lowest retirement wealth, average retirement wealth in the lowest decile, and average retirement wealth in the lowest quartile, are higher for the classic glidepath than the inverse glidepath. The constant mix strategy shows approximately equal values compared to the classic glidepath.

18 Figure 1. Mean retirement wealth of retirement strategies, 1900-2015

5.2.1. Retirement investment strategies with insurance policies for the period from 1900-2015

The results for the CPPI and TIPP are discussed below. The performance of the retirement investment strategies for the period from 1900 to 2015 is discussed in Section 5.2.1. Section 5.2.2. provides a comparison between historical values of each strategy over three time periods.

Table 3. A comparison of CPPI and TIPP, 1900-2015

19 Insurance

policies

CPPI TIPP

Ending retirement assets (World) pension age of 67 Mean $251,737.92 $129,958.68 Median $246,989.35 $43,823.79 Max $1,002,489.52 $373,392.58 AvgD10 $469,467.02 $337,666.01 AvgQ4 $369,881.90 $241,468.19 SD $203,336.92 $122,977.01 Min $27,617.87 $27,849.84 AvgD1 $34,072.61 $30,668.45 AvgQ1 $51,802.88 $34,456.38

The results of table 3 show that the CPPI produces superior wealth outcomes relative to TIPP. The mean retirement wealth of the CPPI is more than 93.5% higher than the TIPP ($251,737.92 versus $129,958.68). The analysis is based on real returns and these are differences in purchasing power.

Furthermore, the CPPI and TIPP have a higher mean retirement wealth than the median retirement wealth. As already mentioned, this indicates a positive skewness in the distribution of retirement wealth, which suggests that these distributions have a higher upside potential than downside potential and it implies that the probability of obtaining at least the mean retirement wealth is lower than 50%. The median retirement wealth of the CPPI is more than 463.5% higher than the TIPP ($246,989.35 versus $43,823.79).

The rest of the upside potential variables considered here are point in the same direction. The CPPI has the highest retirement wealth, average retirement wealth in the highest quartile, and the average retirement wealth in the highest decile.

20 retirement wealth in the lowest quartile are higher under the CPPI than the TIPP. The average retirement wealth in the lowest decile of the CPPI is more than 11% higher than the TIPP ($34,072.61 versus $30,668.45). The average retirement wealth in the lowest quartile of the CPPI is more than 50% higher than the TIPP ($51,802.88 versus $34,456.38).

5.2.2. Retirement investment strategies with insurance policies over time

Above, we discussed the performance of the strategies covering the entire time period from 1900 to 2015. We show the retirement wealth statistics of the CPPI and TIPP over time to investigate the performance between the different strategies. We divided the 75 working lifetimes in three equal parts.

Table 4. A comparison of CPPI and TIPP, 1941-1965, 1966-1990, and 1991-2015

This table shows summary statistics for the CPPI and TIPP evaluated over three periods. The three time periods are from 1900-1965, 1966-1990, and 1991-2015. The first person retired in 1941. The strategies start with a present value of $35,090.83, see the section methodology for the calculation. The CPPI and TIPP are described above in table 3. For each of the two strategies, the statistics describe the series that collects the retirement wealth across the 75 working lifetimes and include the mean, median, lowest (Min) and highest (Max) values, standard deviation (SD), average of the lowest decile (AvgD1) and quartile (AvgQ1) and average of the highest decile (AvgD10) and quartile (AvgQ4).

CPPI TIPP

1941-1965 1966-1990 1991-2015 1941-1965 1966-1990 1991-2015 Ending retirement assets (World) pension age of 67

Mean $128,271.32 $235,472.27 $391,470.16 $39,646.66 $59,312.79 $290,916.59 Median $58,591.60 $241,776.96 $320,952.56 $40,328.57 $34,458.24 $274,304.46 Max $340,404.66 $813,522.47 $1,002,489.52 $51,951.78 $243,472.65 $373,392.58 AvgD10 $310,591.77 $391,055.89 $605,078.76 $47,676.92 $158,776.23 $360,459.47 AvgQ4 $209,199.71 $380,501.40 $466,084.00 $44,276.77 $40,045.49 $341,881.32 SD $109,411.34 $209,064.49 $182,552.00 $6,707.46 $59,785.52 $ 51,924.80 Min $29,593.12 $27,617.87 $185,585.39 $27,849.84 $28,000.73 $225,726.92 AvgD1 $34,615.78 $30,976.49 $240,152.98 $30,408.12 $29,432.12 $234,033.09 AvgQ1 $43,983.92 $35,735.14 $265,782.56 $34,454.52 $31,353.76 $240,780.35

The results of table 4 show that the CPPIproduces superior wealth outcomes relative to the TIPP for each period. The CPPI and TIPP have a higher mean retirement wealth than the median Insurance

21 retirement wealth, excluded CPPI for the period from 1966 to 1990 and TIPP for the period from 1941 to 1965. As already mentioned, this indicates a positive skewness in the distribution of retirement wealth, which suggests that these distributions have a higher upside potential than downside potential and it implies that the probability of obtaining at least the mean retirement wealth is lower than 50%.

The rest of the upside potential variables considered here are point in the same direction. The CPPI has the highest retirement wealth, average retirement wealth in the highest quartile, and the average retirement wealth in the highest decile for each period.

The rest of the downside potential variables considered here are not point out in the same direction for each period. The TIPP produces higher values for the lowest retirement wealth, excluded the period 1941 to 1965. However, the average retirement wealth in the lowest decile and the average retirement wealth in the lowest quartile are higher under the CPPI than the TIPP for each period. As table 4 shows, the TIPP keeps investors less uncertain about their retirement wealth than CPPI for each period, but they do not necessarily provide them with more capital at retirement in bad-case scenarios.

Figure 2 shows the mean retirement wealth of the CPPI and TIPP over time. Over the period 1954-1976 and 1988-2003 the CPPI performs much better than the TIPP. Over the period 1941-1981 the TIPP has bad performances, because the average return of stocks and bonds are very low up to that point. Therefore, the portfolio value will not exceed the adjusted floor many times. The last period of 2004-2015 the TIPP outperforms the CPPI.

Figure 2. Mean retirement wealth of CPPI and TIPP, 1900-2015

22

6. Conclusion

This paper shows the impact of the traditional classic glidepath, the inverse glidepath, constant mix strategy, CPPI and TIPP on the real value of retirement wealth and on the uncertainty concerning the client’s prospective retirement income. The purpose of this paper is to provide a broader perspective on retirement investment plans by considering these three retirement investment strategies and two insurance policy strategies. We contribute to existing literature by investigating a different time period and a different length of working life. We also go beyond the existing literature by investigating whether the insurance policy strategies will improve the results for retirement. We use the real returns of the equity market and bond market for the period 1900 to 2015 to determine the impact on retirement wealth and income. For the retirement investment strategies we used a different approach than the insurance policy strategies, therefore we treat these strategies separately.

23 higher than 50%. The rest of the upside potential variables considered in the paper show the same pattern. For the period from 1991-2015, the classic glidepath has the highest average retirement wealth in the highest decile and average retirement wealth in the highest quartile. Overall, the inverse glidepath strategy and the constant mix strategy usually outperform the classic glidepath when stocks outperform bonds. Second, we show that the CPPI usually outperforms the TIPP. For the period from 1900 to 2015, the CPPI produces superior wealth outcomes relative to TIPP. The CPPI results in a higher retirement wealth than TIPP. The CPPI and TIPP have a higher mean retirement wealth than the median retirement wealth. As already mentioned, this indicates a positive skewness in the distribution of retirement wealth, which suggests that these distributions have a higher upside potential than downside potential and it implies that the probability of obtaining at least the mean retirement wealth is lower than 50%. The rest of the upside potential variables considered here are point in the same direction. The CPPI has the highest retirement wealth, average retirement wealth in the highest quartile, and the average retirement wealth in the highest decile. The standard deviation of the CPPI is higher than the TIPP. In other words, CPPI strategies keep investors more uncertain about their retirement wealth than do TIPP strategies. Investors care about their performance in low return scenarios. The lowest retirement wealth is approximately equal for both strategies. The TIPP keeps investors less uncertain about their retirement wealth than CPPI, but they do not necessarily provide them with more capital at retirement in worst-case scenarios. The rest of the bad scenario variables show a higher value under the CPPI than the TIPP. The average retirement wealth in the lowest decile and the average retirement wealth in the lowest quartile are higher under the CPPI than the TIPP. For three different time periods from 1900-1965, 1966-1990, and 1991-2015 we found some different results as compared to the whole period. The CPPI has a higher median retirement wealth than the mean retirement wealth for the period from 1966 to 1990. The TIPP has a higher median retirement wealth than the mean retirement wealth for the period from 1941 to 1965. Overall, we can conclude that the CPPI results in a better alternative for retirement investment strategy than the TIPP when the stock market outperforms the bond market. Third, as already described above, we find different results for the period 1991-2015, since in this period the bond market outperformed the stock market from 2000-2015. For this period, the traditional glidepath and TIPP would have outperformed strategies that are fully invested in stocks.

24 considerably. The CPPI is a good alternative as retirement investment strategy for risk seeking investors. The CPPI has an extreme high upside potential but the minimum retirement portfolio value is low and therefore a very risky strategy for a retirement investment plan.The CPPI, relative to the TIPP, provides investors with a higher mean and median retirement wealth, higher upside potential, more limited downside potential, and higher uncertainty about their terminal wealth, but are largely limited to how much better, not how much worse.

25

Literature list

Ang, A., 2014. Asset Management: A systematic approach to factor investing, Oxford University Press, Oxford.

Arnott, R., Sherrerd, K., Wu, L., 2013. The glidepath illusion… and potential solutions. The Journal of Retirement 1, 1-17.

Basu, A., Byrne, A., Drew, M., 2011. Dynamic lifecycle strategies for target date retirement funds. The Journal of Portfolio Management, 83-96.

Basu, A., Drew, M., 2009. Portfolio size effect in retirement accounts: what does it imply for lifecycle asset allocation funds? The Journal of Portfolio Management, 61-72.

Dimson, E., Marsh, P., Staunton, M., 2002. Triumph of the Optimists — 101 Years of Investment Returns. Princeton University Press, Princeton.

Estrada, J., 2014. The glidepath illusion: an international perspective. The Journal of Portfolio Management, 52-64.

Estep, T., Kritzman, M., 1988. TIPP: insurance without complexity. Journal of Portfolio Management, 38-42.

Hillier, D., Grinblatt, M., Titman, S., 2012. Financial markets and corporate strategy. McGraw-Hill Higher Education, Berkshire.

Jessen, C., 2014. Constant proportion portfolio insurance: discrete-time trading and gap risk coverage. Journal of derivatives 21(3), 36-53.

Moore, K., 2011. An overview of the U.S. retirement income security system and the principles and values it reflects. University of Kentucky, Lexington.

Perold, A., Sharp, F., 1995. Dynamic strategies for asset allocation. Financial Analysts Journal, 149-160.