Systematic risk in the equity portfolio

A traditional multifactor model

Until the early 1990s, the capital asset pricing model (CAPM) was the dominant model for assessing risk and expected returns on equities. According to the CAPM, the expected return on an equity over and above the risk-free interest rate will depend on the risk premium for equities and that equity’s correlations with the market portfolio, normally known as beta. Within CAPM, two arbitrary equity portfolios can produce different average returns only if the two portfolios have a different beta.

In the 1980s, however, a number of empirical regularities in equity returns were discovered that could not be explained by the CAPM. The “size effect” is an empirical regularity that means that investments in small companies have, on average, produced a market risk-adjusted excess return relative to investments in large companies. Another company characteristic that seems to result in systematic differences in return between equities is the ratio of book value to market value (B/M). Several studies have documented that companies with a high B/M have a systematically higher market risk-adjusted return than companies with a low B/M. This is often referred to as the “value effect” 

In an important article, Fama and French  developed a three-factor model that included factors representing the size effect and the value effect along with the market return. This three-factor model had much greater explanatory power for equity returns than the single-factor CAPM. The theoretical basis for the size and value factors is still unclear, but the Fama-French model has nevertheless become established as a standard in empirical studies of asset pricing.

In their original article, Fama and French(1) used the designations SMB (small minus big) for the factor representing the size effect and HML (high minus low) for the factor representing the value effect. SMB is defi ned as the return on a portfolio with an overweight of the smallest companies and an underweight of large companies. Similarly, HML represents the return on a portfolio with an overweight of the companies with the highest B/M in each size group and an underweight of the companies with the lowest B/M in each size group. Fama and French used a double sort method which was intended to reduce potential size effects in the calculation of the value effect and vice versa. In our factor model, we have used the same method as Fama and French when calculating the factor returns for each country. The global SMB and HML factors have been calculated by fi rst aggregating the country factors up to regional level on the basis of each country’s market value. The regional factors are then weighted together to produce a global factor using the regional weights in NBIM’s equity portfolio.

A fourth empirical regularity which is often included in empirical studies of asset pricing is the “momentum effect”. This effect means that an investment strategy based on buying companies that have produced a high return over the past 3-12 months, and selling companies that have produced a low return during the same period, produces a risk-adjusted excess return. One momentum factor used widely in the literature is UMD (up minus down). This is calculated as the return on a portfolio with an overweight of companies with the highest return in each size group and an underweight of companies with the lowest return in each size group. In our factor model, we use a UMD factor where the factor portfolio at the end of month t is based on the equity return from month t-12 to month t-1.

Equity markets in emerging economies have different risk characteristics to those in developed economies. For a global investment manager like NBIM, it will therefore be natural to include a factor representing emerging economies. In our factor model, we have introduced the factor EMG, which represents the return on a portfolio with an overweight of emerging equity markets and an underweight of developed equity markets.

The equity portfolio’s factor exposures

In our analysis of the equity portfolio’s factor exposures, we have taken the Fama-French model as our starting point and expanded it to include a momentum factor and an emerging markets factor. Table 16-1 shows the results of estimating this fi ve-factor model using monthly data.

The results suggest that the equity portfolio has been exposed to a number of priced risk factors, including the market (MKT) and small companies (SMB). On the other hand, the equity portfolio has had a signifi cant negative exposure to the value factor (HML). This means that the equity portfolio has, on average, been skewed towards equities with a low B/M, often referred to as growth stocks. Alpha, which is the estimated constant in the regression, can be interpreted as the part of the excess return that cannot be explained by passive exposure to the systematic risk factors. For this reason, alpha is often used as a measure of the quality of investment management. The estimate of alpha is positive. It is worth noting that the adjusted coeffi cient of determination R(2) is relatively low: just 35 per cent of the variation in the excess return on NBIM’s equity portfolio can be explained by a traditional fi ve-factor model. By way of comparison, Fung and Hsieh2 found in their study of a large number of equity managers that more than 80 per cent of the variation in excess return can be explained by a traditional four-factor model.

Table 16-1 Estimation results for the period February 1998 to December 2008

The results above show that the equity portfolio has been exposed to a number of risk factors when considering the period as a whole. It may be interesting to see whether this has arisen as a result of a systematic skew towards these risk factors, or whether these exposures have varied over time. Chart 16-1 shows the estimates for the various risk factors over rolling 24-month periods.

Chart 16-1 Coeffcients estimated over rolling 24-month periods

The chart suggests that the equity portfolio’s exposure to most of the risk factors varies considerably over time. Exposure to SMB was high towards the end of 2005 and in 2006. During that same period, the equity portfolio had signifi cant negative exposure to HML. This was due partly to the transfer of capital to external managers with exposure to the small-cap segment, and is therefore partly the result of a conscious investment decision. Both SMB and HML exposure have decreased considerably over the past couple of years. Exposure to EMG increased in 2008. This was due partly to more emerging markets being phased into the benchmark index for the equity portfolio during the year. The estimate of alpha is positive for most of the period but has fallen in the past year.

It may also be interesting to look at whether exposure to the various factors is dependent on market movements. Chart 16-2 estimates alpha and the coeffi cient for MKT for various selections of observations. The first column on the far left of each chart represents the coeffi cient estimate in a regression based on the 20 monthly observations with the lowest market return. As we move towards the right of the chart, more observations based on market returns are gradually included. The last column on the far right of each chart represents the coeffi cient estimate in a regression based on the 20 monthly observations with the highest market return. The column in the very centre of each chart represents the coeffi cient estimate obtained using all of the observations.

Chart 16-2 shows that the alpha estimate is positive in all market regimes. There is also a clear tendency for the alpha estimate to be higher in periods of high market volatility – whether strongly bullish or strongly bearish – than across all observations. The market beta also appears to be positive in most market regimes. However, it appears that the market beta is higher in a bear market and lower in a bull market.

Recent factor models The traditional

Fama-French model has long dominated in both academic studies and practical applications. In analyses of the return on equity funds, excess return is often divided into two components: alpha and beta. Beta is used for the part of the return that is attributable to systematic exposure to the risk factors specifi ed in the factor model, while alpha is any return beyond that.

Many hedge fund strategies are often presented as highalpha strategies without exposure to traditional beta factors. However, several studies suggest that part of the excess return from common hedge fund strategies can be replicated by investing passively in a set of alternative systematic risk factors (3). It has therefore been argued that many hedge funds’ alpha is to some extent a type of beta that traditional factor models are unable to capture. Recent replication models have introduced a number of alternative risk factors relative to the traditional models. In addition, recent factor models have attempted to capture the asymmetrical return profi le that is characteristic of a number of common hedge fund strategies. If we expand the traditional defi nition of beta to include other systematic risk exposures that it is possible to replicate, often known as “alternative beta”, the estimated alpha in a factor model will be reduced.

2008 was a poor year for both NBIM and the hedge fund industry. Although there are big differences between NBIM and the hedge fund industry, it may be interesting to see to what degree NBIM’s equity portfolio has had similar factor exposures to an equity hedge fund. In this analysis, the traditional factor model is expanded to include more recent factors widely used in the literature on hedge fund replication.

A number of academic studies document that liquidity risk plays a signifi cant role in the pricing of equities(4). Gibson and Wang (5) find empirical support for the interpretation of excess return from several common hedge fund strategies as compensation for accepting liquidity risk. Such exposure might, for example, arise as a result of a hedge fund playing on what are known as reversal effects, where the manager systematically buys equities that have decreased greatly in value and sells comparable equities that have increased greatly in value. Liquidity risk has many dimensions, and there are therefore a number of different risk indicators. Gibson and Wang look partly at an indicator based on Amihud (2002) (6). This liquidity measure is based on the relationship between absolute return and trading volume: the greater the change in price triggered by a given trading volume, the more illiquid a stock will be. In our model, we have chosen to use a size-adjusted indicator of liquidity risk based on Amihud (2002). This factor (ILL) is the return on a portfolio with an overweight of illiquid equities in each size group and an underweight of liquid equities in each size group.

We have included two factors with a non-linear return profi le. The fi rst (CRY) is intended to represent carry trades. This expression originates in fi xed income management, but is often now used as an umbrella term for strategies that systematically collect risk premiums. These strategies are often compared with issuing insurance: there can be long periods of simply collecting premiums, but there can be a big loss if the sum insured has to be paid out. Within equity management, there are several examples of strategies that can be characterised as carry trades. These include arbitrage in takeover situations, with a systematic overweight of companies that are being acquired and an underweight of the acquiring company (7). In our analysis, we have used the return on a strategy that is systematically long a high-yielding currency (NZD) and short on a low-yielding currency (JPY) as a proxy for carry trades. The other factor with a non-linear return profi le (VOL) is the return on a strategy that systematically issues put options. With this strategy, it may be possible to collect option premiums for long periods. Should the equity market take a tumble, though, there will be an obligation to purchase equities at above the market price and so take a loss. Common to CRY and VOL is that these strategies have a very skewed return distribution, with many observations that are slightly positive and a few that are deeply negative.

Table 16-2 compares NBIM and the hedge funds when it comes to the different risk factors. The hedge funds seem to have greater market exposure than NBIM, while NBIM seems to have greater exposure to HML than the hedge funds. There are no big differences for the other traditional factors. However, there are signifi cant differences between NBIM and the hedge funds when it comes to the new factors. NBIM seems to have less exposure to both liquidity risk and the asymmetrical risk factors. It is also worth noting that NBIM has generated signifi cantly more alpha than the hedge funds in an expanded eightfactor model.

Table 16-2 NBIM versus equity hedge funds in the period April 2003 to December 2008

Conclusion

NBIM’s equity management has been built up with a view to generating excess return through fundamental stock analysis within a number of specialised investment mandates. With this kind of framework, the individualmanager will often hunt for mispriced stocks in market segments that are less effi cient. This might be in the small-cap segment, and sometimes also in emerging markets. At the same time, active positions have a tendency to be fi nanced by selling large companies where the fi nancing costs are lowest. Active equity management will therefore have an inherent tendency to create exposure to the traditional risk factors. This can also be seen with most other equity managers (8). Given NBIM’s investment philosophy, we must therefore expect to see exposure to the traditional risk factors when the equity portfolio is viewed as a whole.

Exposure to systematic risk factors may also be an intentional effect of various investment decisions. One example of this is the allocation to external managers with exposure to the small-cap segment which affected the equity portfolio’s exposure to SMB and HML in 2005- 06. The important thing for NBIM is not, therefore, to eliminate all exposure to known risk factors at all times. Instead, considerable importance is attached to taking a conscious position on all risk exposures in the equity portfolio at any one time, whether these exposures are intentional or unintentional, and whether they are to traditional or alternative risk factors.

1 Fama, E.F. and K.R. French (1993): “Common Risk Factors in the Returns on Stock and Bonds”, Journal of Financial Economics, 33(1), 3-56.

 2 Fung, W. and D.A. Hsieh (2006): “The Risk in Hedge Fund Strategies: Theory and Evidence from Long/Short Equity Hedge Funds”, Duke University, Working Paper.

3 See, for example, Jaeger, L. (2008): “Alternative Beta Strategies and Hedge Fund Replication”, Wiley Finance.

4 Acharya, A. and L. Pedersen (2005): “Asset Pricing with Liquidity Risk”, Journal of Financial Economics, 77, 375-410.

5 Gibson, R. and S. Wang (2008): “Hedge Fund Alphas: Do They Refl ect Managerial Skills or Mere Compensation for Liquidity Risk Bearing?”, Swiss Finance Institute Research Paper No. 08-37.

6 Amihud, Y. (2002): “Illiquidity and Stock Returns: Cross-section and Time-series Effects”, Journal of Financial Markets, 5, 31-56.

7 Mitchell, M. and T. Pulvino (2001): “Characteristics of Risk and Return in Risk Arbitrage”, Journal of Finance, 56, 2135-2175.

 8 Fung, W. and D.A. Hsieh (2004): “Extracting Portable Alphas from Equity Long/Short Hedge Funds”, Journal of Investment Management, 2(4), 1-19. Fung, W. and D.A. Hsieh (2006): “The Risk in Hedge Fund Strategies: Theory and Evidence from Long/Short Equity Hedge Funds”, Duke University, Working Paper.