# Alternative Approach Conclusion

# Conclusion

When applied outside the confines of a single market e.g. to the construction of a multi-asset portfolio, the CAPM is subject to criticism. Most importantly, requiring the definition of an appropriate market proxy renders the CAPM inapplicable to investment decisions across asset classes. This, combined with the lack of evidence in support of a linear relationship between risk and return, promoted the search for an alternative model.

First suggested by Markowitz [1959], but dropped in exchange for the computationally more efficient mean-variance model, the semi-variance and later, downside-variance models were attempts to accommodate the notion that investors require a target rate-of-return. However, under the assumption of normality, downside-variance models are subject to the same criticism as the CAPM. They also rely on the unacceptable assumption that investors are risk-neutral above a target rate-of-return. This necessarily led us to attempt the definition of an alternative model of asset pricing.

It has been suggested that investors should be more concerned with the probability or chance of incurring a loss, or a smaller than expected return from an investment decision, than total variance of returns. As such, the proposed DRT model is an attempt to provide a more accurate description of investor preferences.

The DRT model accommodates the notion of downside-risk-aversion and accounts for returns distributions above the target rate-of-return. Unlike the CAPM, the proposed model places greater importance on returns below a specified target rate-of-return and allows the approximation of a wide variety of attitudes towards the risk of falling below the target return.

The matching of long-term liabilities is fundamental to the management of life insurance and pension funds. As a result, the arguments in favour of using the DRT model as a method of controlling risk are particularly relevant to life and pension fund managers. With its approach focusing on returns measured against the main source of pension fund risk i.e. not obtaining a minimum actuarially defined rate-of-return, it provides a more accurate model of institutional preferences.

The DRT model offers a framework for integrating alternative assets, such as those with asymmetric payoff distributions, and provide a greater level of risk control. It also renders a customised approach to risk management, allowing an investor to explicitly define risk preferences, through *κ* and *α*. It may also provide a more realistic measure within the realms of performance evaluation.

Investors have been shown to commonly frame and evaluate risky prospects in terms of their anticipated gains or losses rather than in terms of final 'portfolio' positions, defined by combining the prospects in hand with all other holdings. Furthermore, investors often segregate their investments into separate mental accounts (e.g. speculative investments, works of art, savings) according to functional or causal considerations (Kahneman & Tversky [1984]). The DRT model allows each to be framed in terms of a different target rate-of-return and degree of risk-aversion.

This chapter tested the hypothesis that the proposed DRT model offers a statistically significant alternative to either the MPI model or the Sharpe performance measure. For the less risk-averse investor, DRT portfolios significantly outperformed the MPI portfolios over the period 1977-1994. However, the variance of the most risk-averse investors portfolio under the DRT model is much higher than that of traditional model's. As discussed, the variance is a measure of both upside and downside volatility and thus may not be an accurate reflection of risk. This is well illustrated when comparison is made between the location of the two returns distributions. The density of the DRT distribution is negatively skewed, with its lower quartile approximately equal to the MPI portfolios mean. These results being consistent with the DRT model's specification; the minimisation of downside-variance. This having been said, Sharpe's performance measure still suggests that together with the less risk-averse DRT portfolios, they are all superior to those constructed under the MPI model.

The DRT model reduces the risk of downside participation, and is an extension to the stop/loss idea, in that it weights the total distribution according to investors risk preferences. Most importantly, the model reduces the traditional importance of volatility.

Within a national context, and in line with conventional models, including real estate within a multi-asset portfolio was shown to substantially improve risk-adjusted returns.

However, the proportion of real estate allocated was less under the DRT model than the conventional MPI model. This result was due to the reduced importance in the model of variance, which in turn reduced the diversification benefits often associated with real estate investment and rewarded under conventional models. Instead of focusing on an asset's contribution to the mean-variance trade-off of a portfolio, the DRT model is concerned with the trade-off between downside-variance and upside-variance, where variance above a target rate plays a positive rather than negative rôle.

This was illustrated upon widening the investment universe to include Far East equities. Under the DRT model, investors switched out of real estate and into Far East equities. They thereby sacrificed a reduction in the volatility of their portfolios for an increase in expected returns, thus improving the probability of achieving their target rate-of-return. This was in marked contrast to the proportion of real estate held under the conventional MPI model, and provides a more accurate picture of current life and pension fund practice.

The DRT performance measure was also tested on a sample of quoted UK real estate companies over the period 1984-1994. When compared with Sharpe's measure, the results showed that the DRT measure was a statistically significant alternative. However, due to sample size the Wilcoxon signed rank test failed to provide strong evidence that there is a significant difference between Sharpe and DRT rankings. This was due to the test's limited power, hindered by negative excess returns and the consequential lack of valid Sharpe measures.