Comparing the performance of retail unit trusts and capital guaranteed notes

WORKING PAPER Comparing the performance of retail unit trusts and capital guaranteed notes by Andrew Clare & Nick Motson 1 1 The authors are both members of Cass Business School s Centre for Asset Management Research (CAMR), Cass Business School, London. EC1Y 8TZ. Their email addresses are respectively: Andrew Clare (a.clare@city.ac.uk); and Nick Motson (n.e.motson@city.ac.uk).

1. Introduction There has been increasing interest in the investment acumen of retail investors in the academic literature. The received wisdom is that retail investors tend to buy at the top and sell at the bottom of the equity market cycle. Until recently it has been quite difficult to test this hypothesis. However with the increasing availability of high quality fund flow data it has been possible to analyse the investment decisions of both retail and institutional investors. The more we understand about the behavioural aspects of retail investment patterns, the more likely it is that the finance industry will be able to produce investment products that can eliminate the wealth reducing features of this behaviour. So what is the evidence for retail investor skill, or lack of it? A study by Dichev (2007) 2 who uses index level data finds strong evidence to suggest that these timing decisions have been very costly for US equity investors. Their results indicate that over the period from 1926 to 2002 the annual cost to the investor was around 1.3% per annum. This figure represents a massive loss in wealth compounded over this period. Dichev also identifies a negative correlation between flows and past returns, but a positive correlation between flows and future returns, which together suggest that investment in US equities tended to increase after good returns and before a period of poor returns hence explaining the underperformance relative to a buy and hold strategy. However, Dichev s use of index level data makes it difficult to understand how much weight we can put on these results. Other researchers have used fund level data, which is more appropriate for analysing the question at hand. These researchers all calculate an indicator referred to as the performance gap to assess the differences between buy and hold strategies and those that involve retail investment timing decisions. 2 Frazzini and Lamont (2006) provide some early evidence that retail investors do indeed invest at the wrong time. They find that the median investor sells as the market troughs and tends to buy at equity peaks, hence confirming the anecdotal evidence of retail investment patterns. 2

In a study of US mutual fund investor behaviour from 1991 to 2004 Friesen and Sapp (2007) find that the typical investor loses 1.56% per year due to the timing of their investment decisions. And since they use disaggregated data they are able to identify, for example, that this performance loss averages 0.13% per month for actively managed funds but only 0.05% per month for passive funds. They also find that there is a greater degree of poor investment timing associated with better performing funds. They show that the performance loss of the average investor in the lowest decile of funds, by alpha, experienced a loss of 0.068% per month, while the same figure for the top decile of funds was 0.378% per month. These results suggest that investors are attracted to the top performing funds at the worst time, that is, towards the top of the market, or indeed are selling funds that performed well in an equity market rally at the bottom of this cycle. They also found that evidence of poor investment timing decisions was almost entirely absent in the context of bond and money market mutual funds. This suggests that the behavioural biases that lead to the performance gap are an equity market phenomenon. Dichev and Yu (2009) also investigate the issue of investor investment timing, but in the context of hedge fund investing. The buy and hold returns reported by the funds studied in the paper are found on average to be around 4.0%pa higher than those achieved by the median investor as a result of their net investments in to the funds. Thus the high alpha that the median investor believed that they were accessing over this period from this investment category may have been almost entirely lost in the timing of their investment decisions. In line with the results of Friesen and Sapp (2007) for mutual funds, Dichev and Yu also found that the performance gap was even larger for the top performing hedge funds. The performance loss for these star funds was an astonishing 9%pa. Using data collated by the Investment Management Association (IMA) 3 that spanned the period from 1992 to the end of 2009 Clare and Motson (2010) examined market level data on 3 The IMA is the trade body for the UK's asset management industry (http://www.investmentuk.org/). 3

the net investment into broad categories of UK mutual funds (known in the UK as unit trusts). Their results, the first of their kind on non-us mutual funds, were broadly in keeping with those achieved using US mutual fund data. As such their work suggests that the performance gap phenomenon is probably global rather than being confined to any one set of investors from a particular market. Clare and Motson find that on average UK retail investors have lost performance equivalent to just under 1.2% per year over the eighteen year period of their study. Although 1.2% may not sound very high, compounded over 18 years it represents a cumulated underperformance of 20%, compared with a simple buy and hold strategy. By distinguishing between retail and institutional flows into these funds, Clare and Motson also show that the UK s performance gap phenomenon is a feature that is almost entirely due to retail investor behaviour, since the performance gap for institutional flows is virtually 0.00%pa. The performance gap phenomenon, whereby retail investors seem to make sub-optimal, wealth reducing, investment timing decisions is a feature of at least the US and UK mutual fund industries and is probably a global phenomenon. The challenge for retail investment product providers is therefore to develop products that can help minimise these costly behavioural biases. One potential approach is to design investment products that as far as possible limit the ability of investors to time the market as far as possible effectively forcing them in to a buy and hold strategy. The unfortunate downside to this is that investors would not be content to hold an investment product that might lock them into a falling market, giving them no opportunity to sell out before this point even though most of the evidence discussed above suggests that they tend to sell too late anyway. Over recent years retail investment product providers have designed a mind-bogglingly wide range of investment vehicles that are referred to collectively as structured products. These are usually a combination of a cash investment and a position in one or more derivatives, usually options. Although, the very wide range of these products makes it difficult to 4

generalise, many of them have been designed explicitly to protect investors either completely or partially from downside risk. They therefore often address one of the biggest issues identified by researchers in the area of behavioural finance that is investor loss aversion. Researchers have found that investors have an asymmetric approach to gains and losses, in that they prefer to avoid losses more than they prefer equivalent gains 4. Since these investment products are also usually designed to be held for a fixed period of time, even though investors can usually redeem their investment within the originally intended investment horizon, they might potentially reduce the temptation of investors to try time the market, but simultaneously protect the downside. In this paper we construct two generic structured products that each have a fixed investment horizon of five years and offer downside protection for the investor. They are generic examples of what are referred to as capital guaranteed notes. Through a series of empirical simulations we compare their performance over time with the performance of a long only investment in equity markets where we superimpose the investment timing decisions of the median UK retail investor identified by Clare and Motson (2010). We therefore offer the first comparison of an investment in a generic equity-based capital guaranteed note with the median investor s investment in the equity market via a mutual fund. The rest of this paper is organised as follows: in Section 2 we describe the construction of the generic capital guaranteed notes, and the data used to value these notes over time; in Section 3 we present the comparison of the notes with equivalent investments in the equity market, where we have accounted for the median UK investor s investment timing decision; finally, Section 4 concludes the paper with some thoughts about possible areas of future research. 4 For the original source of these and other related ideas see Kahneman and Tversky (1979). 5

1. Two capital guaranteed notes To compare the median retail investor s investment experience in equity unit trusts with that that might be achieved by an investment product that removes the need or temptation to time the market and simultaneously protects investors from downside risks over the period, we construct two very generic capital guaranteed notes whose eventual payouts are dependent upon the performance of the FTSE-100. 1.1. Capital Guaranteed Note 1 (CG1) For each 100 worth of CG1 purchased by an investor in any month X% of the 100 is invested in a highly rated zero coupon sterling corporate bond, with a maturity of five years and face value of 100. The value of this bond at the time it is purchased as part of the note is dependent upon prevailing five year, zero coupon, corporate bond yields. For example, suppose this rate is 10%, then the purchase price of the zero coupon bond with a face value of 100 will be: Price of zero coupon bond = 100/(1+10%) 5 = 60.65 This leaves 39.35 which can then be used to purchase a five year, European, at the money call option on the FTSE-100. This remaining cash may buy more or less than 100 worth of exposure to the FTSE-100. For example, let us suppose that 20 will give the holder of the option the right to buy 100 worth of the FTSE-100 at an index level of 2570, in five year s time. The pay off profile for this fairly standard option is shown by the blue line in Figure 1. 6

Figure 1: CG1 Call payoff 50.0 Pay off per 100 invested 40.0 30.0 20.0 10.0 Pay-off per 100 CG1 call pay off 0.0 2390 2450 2510 2570 2630 2690 2750 2810 2870 2930 2990 3050 3110 FTSE-100 The at-the-money call option will have a strike price of 2,570 index points. At the end of the five years if the FTSE-100 index closes above this level then there will be a positive pay-off for the investor. Effectively for every percentage point that the FTSE-100 closes above this level in five year s time, the investor gains 100 multiplied by this percentage gain. So for example, if the FTSE-100 closes five years after the note is purchased at 3084, 20% higher than 2,570, then the call option will pay out 20 (20% of 100). However, in our example above the note has 39.35 available to purchase the option. In other words, it can buy almost twice the exposure to the market. So for every percentage increase in the FTSE- 100 s level at the expiry of the option compared to its level when the note is purchased, the call option will pay out almost double this amount. So in our example rather than receiving 20, the investor would receive almost 40 on every 100 invested if the FTSE-100 ended the five year period 20% higher at 3084. In effect for a rise in the market the holder of the option has a leveraged investment in the FTSE-100. The payoff for the option contained within the note is shown by the red line in Figure 1. However, in the event that the FTSE-100 ends below the strike level of 2,570, the call option expires worthless, and the investor effectively loses the non-refundable 39.35 paid originally for the option. The net effect of this combination of an investment in a zero coupon bond and FTSE-100 equity call options, all wrapped up in this one note, is as follows: 7

In the event that the FTSE-100 is higher after five years than its level at the start of this five year period, the investor receives: 100 from the zero coupon bond, plus 100 multiplied by the % increase in the FTSE-100 over this period, multiplied by the option s leverage In the event that the FTSE-100 is lower after five years than its level at the start of this five year period, the investor receives: 100 from the zero coupon bond This explains the name of this product capital guaranteed. After five years the investor receives their initial investment of 100, or a greater sum, depending upon the performance of the FTSE-100 over this period. More importantly, investors purchasing this note are protected from a fall in the equity market, to which an outright investment in equities would expose them. 1.2. Capital Guaranteed Note 2 (CG2) The second note that we construct is very similar to CG1. It again consists of an investment in both a zero coupon bond and the purchase of a call option on the FTSE-100. However, in this case the purchase of the call option is just sufficient to gain exposure to 100 worth of the FTSE-100. In other words, for every percentage increase in the FTSE-100 above its starting, or strike value the investor receives 100 multiplied by this increase. This means that the payoff for the investor from the call option will be represented by the blue line in Figure 1. 8

Suppose that the cost of this option is 20, this means that 80 is left over to invest in the zero coupon bond. If we assume that the prevailing rate of interest for five year zero coupon bonds is 10% once again, this means that after five years an investor will receive the following payout from the zero coupon bond: Payoff from zero coupon bond = 80 x (1+10%) 5 = 128.84 The net effect of this combination of an investment in a zero coupon bond and FTSE-100 equity call options, all wrapped up in this one note, is as follows: In the event that the FTSE-100 is higher after five years than its level at the start of this five year period, the investor receives: 128.84 from the zero coupon bond, plus 100 multiplied by the % increase in the FTSE-100 over this period In the event that the FTSE-100 is lower after five years than its level at the start of this five year period, the investor receives: 128.84 from the zero coupon bond In this case the guaranteed amount is higher than the initial investment of 100. The guaranteed minimum is 128.84. The upside from this structure is lower since there is no leverage, however the investor still receives 100% of any rise in the FTSE-100 over the five year note period and is protected from falls in the value of the FTSE over this period. 9

1.3. Data and pricing the components of CG1 and CG2 Using the two structures described above we calculate the return that an investor in each of these notes would achieve over the five year maturity of the note. We calculate this return on a rolling, monthly basis from January 1992 to December 2009. This means that the first CG1 and CG2 notes mature in January 1997, while the last ones are issued in December 2004. The performance of each of the notes (two created each month) will depend upon the performance of the FTSE-100 over the relevant five year investment horizon, and the prices paid for the zero coupon bond and call options at the start of each of these periods. To price the zero coupon bonds over time we need to identify the yield on such bonds, with a consistent rating, going back to 1992. Unfortunately the sterling corporate bond market was relatively underdeveloped over most of this period. Furthermore, zero coupon bonds are not issued on a regular basis by corporations. To overcome these issues we extracted the five year, sterling zero coupon rate embedded in the sterling swap curve 5 on a monthly basis from January 1992 to the end of our sample period. This allows us to find a fair price for a five year zero coupon bond for every note that we construct. The implied rating of the bond would therefore be equivalent to the average rating of the pool of banks that determine LIBOR over time, which is approximately AA. Hence, our notes are observationally equivalent to those that might be issued and supported by a AA credit rated issuer. NB: The issue of the credit support within structured notes is not a trivial one. In essence the notes that we describe above embody counterparty risk. If the issuer of the zero coupon bond were to default on its bond obligations then the downside protection afforded by the bond (or guarantee) would be impaired. In the simulations that follow we assume that the guarantor does not default on this obligation. This must be borne in mind when our results are considered. 5 It is a relatively simple, mechanical task to extract zero coupon rates from par swap curves. 10

As well as having to price the zero coupon bond we also need to price the European call option on the FTSE-100 for each note that we create. We need to price this option because there is no readily available price for a five year European call option on the FTSE-100. To find a price we therefore use the well known Black-Scholes equation. To implement this pricing technique we need additional information. The option premium (P) is a function of a number of inputs: P = f(s, X, r, t, σ) where S is the level of the index on the start date of the note; X is the strike price of the option, which in our case equals S; r is the funding rate over the term of the option; t is maturity of the option; and finally, σ is the annualised volatility of the FTSE-100 over the life of the option. Finding a value for σ requires us to make an estimate of what would be the market s view of the future volatility of the FTSE-100 over the next five year s. We overcome this issue by using the historic volatility of the FTSE-100 immediately prior to the issuance of the note. Figure 2 illustrates how close our measure is to the volatility implied in FTSE-100 option prices from a more recent period. The green line in the chart represents our estimate of implied volatility. We compare this with the market s estimate of implied volatility, represented by the blue line. If the data represented by the blue line in Figure 2 were available back to 1992, we would not have needed to estimate our own measure of volatility. 11

Figure 2: Historic volatility measure versus implied volatility of FTSE-100 100 80 Implied Vol Hisotrical Volatility Implied volatility, %pa 60 40 20 0 Sep 07 Dec 07 Mar 08 Jun 08 Sep 08 Dec 08 Mar 09 Jun 09 Sep 09 Dec 09 Mar 10 1.4. Simulation methodology Having estimated both the price of a five year zero coupon bond and the price of a European call option on the FTSE-100 from 1992 to the end of our sample, we can calculate the features of both of the five year notes described above. Essentially we issue these two notes at the start of each month in our sample and calculate their payoff at the end of each five year period. By doing this we can calculate the average return over time that an investor might expect to receive from investing in such products over a business cycle. This allows us to compare this return with the return that could be achieved by investing in the equity market directly, but where we take account of the timing decisions of the typical investor. To illustrate the methodology we can provide the details of the first two notes that we issue in January 1992. CG1 Jan 1992: The note is issued at a price of 100. The price of five year zero coupon bond with par value of 100 is 61.88, giving an annualised yield of approximately 9.6%. The price of a five year at-the-money, European call option on the FTSE-100, with a strike price of 2,571 to buy 100 worth of the FTSE-100 is 18.35. This means that 2.08 of these calls can be purchased per 100 worth of the note, giving a 208% leveraged exposure to the 12

upside of the FTSE-100 over the next five years. This leverage will vary over time. It will depend upon the price of the bond, which will in turn depend upon prevailing interest rates. It will also depend upon the price of the option which will vary according to changes in interest rate environment and the volatility of the underlying market. Figure 3 shows how the participation in the equity market changes over time. The average participation rate over this period for a note with CG1 s features is 159%, but there are times when it as high as 250% and as low as 50%. This participation rate will tend to be particularly high when interest rates and option premia are low both low. 300% Figure 3: Participation rate over time for CG1 250% Participation of CG1 200% 150% 100% 50% 0% 1992 1994 1996 1998 2000 2002 2004 CG2 Jan 1992: The note is issued at a price of 100. The price of a five year at-the-money, European call option on the FTSE-100, with a strike price of 2,571 to buy 100 worth of the FTSE-100 is again 18.35. This leaves 81.65 to be invested in a five year zero coupon bond with par value of 100. After five years this 81.65 invest in a zero coupon bond with an initial yield of 9.6% will be worth 131.96. This represents the guaranteed floor of the note. However, this floor will vary over time with interest rates and with the option premium. Figure 4 shows how the floor changes over time. The average floor is 111.5% of the initial investment of 100. As the chart shows there are times when the combination of financial prices means that the product is unable to guarantee 100% of the initial investment. In 13

practice, at these times product providers would be unlikely to issue such bonds, but we include these notes in our analysis for completeness. Figure 4: Capital guarantee over time for CG2 140% Capital guarantee of CG2, % of initial investment 120% 100% 80% 60% 1992 1994 1996 1998 2000 2002 2004 2. Investment timing versus capital guaranteed notes In this section of our paper we compare the performance of the notes described above and calculated on a rolling basis from 1992 to the end of our sample period, with those achieved from investing directly into the UK equity market (represented here by the FTSE-100). We calculate the latter as follows. Using the scaled flows calculated from the IMA data presented in Motson and Clare (2010) we simulate the investment experience of the typical retail investor. Specifically, for each five year period we start with an initial capital of 100 and assume that the investor receives each month the total return of the FTSE 100 index including dividends. We also assume that each month the investor either invests or withdraws capital in exactly the same proportions as in the IMA retail investor data. We then calculate the money weighted return for each five year period by solving for the internal rate of return in the same way as in Motson and Clare (2010). 14

The mean return generated from this procedure is approximately 11bp per month or 1.4% per annum lower than the simple buy and hold return. This result matches with our previously documented findings of the performance gap which is predominantly driven by retail investors allocating more capital following periods of strong equity performance and withdrawing capital following periods of poor performance. 40% Figure 5: Capital Guarantees versus equity timing Panel A: CG1 Panel B: CG2 40% 35% CG1 FTSE Total Return With Bad Timing 35% 30% 30% CG2 FTSE Total Return With Bad Timing 25% 25% 20% 20% 15% 15% 10% 10% 5% 5% 0% -6% -4% -2% 0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% 22% 24% 26% 28% 0% -6% -4% -2% 0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20% 22% 24% In Figure 5 the blue bars in each panel represent the distribution of five yearly returns that investors would experience from investing in the FTSE-100, taking account of their timing decisions. In this Figure we also plot the distribution of returns for investments in both CG1 (Panel A) and for CG2 (Panel B). The first thing to notice is how the distribution for both capital guaranteed notes is truncated at 0. This is of course the point of these notes. A five year direct investment in the FTSE-100 over this period would have produced a negative return on 18% of all occasions. For CG1 on 34% of all occasions the pay off would have been the original amount of 100. However, on 66% of all occasions the return was positive and on 47% of these occasions the investor would have experienced a double digit return and on 18% of all occasions the return experienced was greater than the maximum achieved by a more straightforward five year 15

investment in equities over this period. The higher return on these occasions is a function of the leverage in CG1, that is, the investor gains more than 1% for every 1% increase in the FTSE-100 over the five year investment horizon. For CG2 there are fewer occasions where the investor simply receives their money back; 5% compared with 34% for CG2. This is because the guaranteed amount is usually higher, that is, on most occasions the zero coupon bond pays back more than 100% of the initial investment of 100. However, the downside of this higher protection is less equity upside, since there is no leverage in this product. For every 1% rise in the FTSE-100 over this period the investor receives 1%. On 45% of occasions the investor receives at least a double digit return, but on no occasions is the return greater than 20%. For CG1 returns are greater than 20% on 30% of all occasions. Table 1: Risk statistics Notes: This table presents descriptive statistics for the series of annualised returns presented in Figure 5. Long only CG1 CG2 Average 7.91% 9.72% 8.04% Min -7.94% 0.00% -1.01% Max 21.81% 27.82% 20.32% St. Dev. 8.70% 9.94% 6.59% Down Dev. 1.75% 0.00% 0.14% In Table 1 we present summary statistics for the three sets of returns. The long only equity investment produces the lowest average return and has the largest five yearly loss. However, the standard deviation of CG1 is higher than for the long only equity investment. At first sight this seems odd, since (by definition) the negative tail is excluded from the possible return outcomes. The answer is clearer when we calculate downside deviation, shown in the last row of Table 1. Downside deviation is a measure of risk that focuses on the component of risk that investors focus on most, that is, those occasions when they experience a loss. There are no occasions when this happens for CG1 and only a few (7) 16

when this happens for CG2. With regard to the latter it only occurs when the guarantee is less than 100%. The larger standard deviation of CG1 is due to the wider dispersion of positive returns that can be seen in Panel A of Figure 5. 3. Summary In this paper we have integrated the results of Clare and Motson (2010), who had previously established the typical return experience of a retail investor in UK mutual funds, with the sort of return experience that these investors might have experienced had they instead purchased generic capital guaranteed notes. This is the first piece of academic research to our knowledge that has brought these two issues together. We choose to compare the typical return experience of an investor with the two capital guaranteed notes used here, because we felt that the notes as we have constructed them deal with two important issues. First, the evidence from behavioural finance literature, that investors are loss averse. And second, the issue of the performance gap that has been documented in both the UK and US which arises from poor investment timing decisions amongst retail investors (though not institutional investors). Ultimately however, the choice between investing directly in equity mutual funds which brings the temptation to time the market, and capital guaranteed notes of the kind considered here will be depend very much upon the risk preferences of individual investors. Those that are confident of their market timing abilities and that worry about the counterparty risk involved in structured notes will presumably choose the former. While those that are comfortable with counterparty risk, but who wish to avoid generalised downside equity market declines will presumably choose the latter. However, our work here, and in particular the results presented in Figure 5 and Table 1, provides useful information for those considering both alternatives. 17

4. References Clare, A and N. Motson, Do UK retail investors buy at the top and sell at the bottom? (2010), CAMR Working Paper, London. Dichev, Ilia D., 2007. What are Stock Investors Actual Historical Returns? Evidence from Dollar-weighted Returns, American Economic Review 97, (1) March: 386-401. Dichev, D. and G. Yu, Higher risk, lower returns: What hedge fund investors really earn, (2009), Goizueta Business School at Emory University, Working Paper. Frazzini, Andrea, and Owen A. Lamont, 2008. Dumb Money: Mutual Fund Flows and the Cross-section of Stock Returns, Journal of Financial Economics (88): 299-322. Friesen, Geoffrey C., and Travis R. A. Sapp, 2007. Mutual Fund Flows and Investor Returns: An Empirical Examination of Fund Investor Timing Ability, Journal of Banking & Finance 31, (9): 2796-816. Kahneman, D. and A. Tversky, Prospect Theory: An Analysis of Decision under Risk, Econometrica, Vol. 47, No. 2 (Mar., 1979), pp. 263-292. 18