**"risk market"**

## Hedge Fund Strategies (Part 4) –Hedged Equity Market Neutral

*by Eric Bank on April 7, 2011 · No Comments · in Documenting the Search for Alpha*

Traders take positions in pairs of similar stocks, longing the “undervalued” one and shorting the “overvalued one”, thereby placing a bet on the ultimate outperformance of the long position.

We now turn to equity trading strategies that attempt to decouple market movements from portfolio returns. Traders take positions in pairs of similar stocks, longing the “undervalued” one and shorting the “overvalued one”, thereby placing a bet on the ultimate outperformance of the long position. By using equal dollar investments on each member of the trading pair to effect an overall neutral long/short position, the trader is looking to remove beta as a factor affecting portfolio performance. The pair of stocks is usually composed of close competitors in the same market, and therefore presents the same country risk, currency risk, market capitalization risk, etc. By attempting to limit risk exposure to the relative merits of the two stocks, *hedged equity market neutral strategy* (HEMNS) can be equally attractive in up and down markets.

HEMNS is usually considered a long-term strategy, and may utilize a mix of fundamental and technical analysis. An alternate form of HEMNS is *statistical arbitrage *(stat arb), in which the pair of positions is determined through the use of *technical and quantitative analysis*. The goal is to take positions in which a traders proprietary algorithms show a pair of stock to be temporarily mispriced (one too high, one too low); the trader is betting that the stocks will shortly* revert to their mean price*, at which point the trade is liquidated.

Example

In this example, the trader opens the position with equal dollar amounts of a pair of closely-related auto parts stocks. During the period, each stock pays a dividend. The position is put on for 90 days. Each stock pays a dividend during the period. After accounting for transaction costs, financing costs on the short position, and dividend payments, the strategy provided an annualized return of over 42%. (This is for purposes of illustration only).

For HEMNS to work, there must be a short-term suspension of the efficient market hypothesis (EMH), since a profit opportunity only arises if there is a difference between a stock’s theoretical fair market value and its current price. However, there can be multiple factors at work in HEMNS besides “incorrect” pricing. For instance, style risk arises from choosing assets according to value, capitalization, or momentum. There are also risks due to liquidity, leverage, interest rates, etc. Since each of these risks are rewarded by specific premia, it may be difficult to say for certain that HEMNS returns are due solely or even largely to an asset manager’s ability to differentiate overvalued and undervalued stocks. Such ability, if consistently manifest over time, could be termed alpha, as it may signify returns due to a manager’s skill, not just risk exposure.

However, studies of several paired-equity styles, such as high-value/low value, winning momentum/losing momentum, and small cap/large cap, have shown systematic risk premia available that are not captured by the standard CAPM, as we have discussed in previous articles. Some argue that these risk premia are due to factors like recession risk, bankruptcy risk, and liquidity risk. Others favor behavioral finance, which claims that market inefficiencies are due to suboptimal investor decisions, as an explanation. Investors may not really care, as long as returns are good.

Later on in this series, it will be our task to see if we can replicate HEMNS results without any special stock-picking skill. But we have many more strategies to examine first. We will continue our tour of hedge fund strategies next time with equity hedged short selling.

## Capital Asset Pricing Model, Part Two – Systematic Risk

*by Eric Bank on January 18, 2011 · No Comments · in Documenting the Search for Alpha*

We are reviewing the underlying assumptions made by the Capital Asset Pricing Model (CAPM). Recall from last time the assumption that returns are distributed normally (i.e. a bell-shaped curve) and how this fails to account for skew and fat tails. Today we’ll look at CAPM’s assumption that there is but a single source of priced systematic risk: market beta.

We are reviewing the underlying assumptions made by the **Capital Asset Pricing Model (CAPM)**. Recall from last time the assumption that returns are distributed normally (i.e. a bell-shaped curve) and how this fails to account for **skew** and **fat tails**. Today we’ll look at CAPM’s assumption that there is but a single source of priced **systematic risk**: market **beta**.

Beta, of course, refers to the correlation between the returns on an asset and the returns on the broad market. Specifically, it is defined as:

βi = Cov(Rm, Ri) / Var(Rm) for asset i

that is, the **covariance** of the asset’s returns with the those of the market divided by the **variance** of the market returns. Another way to think about beta is as a discount factor: when divided into an asset’s expected return, it adjusts the expected return so that it equals the market’s expected return.

By making this assumption, CAPM is able to simplify the universe of different risks undertaken by a portfolio, such as a hedge fund, to one global number. That’s good for ease of calculation but bad for reflecting reality. It is also assumed that all non-systematic risk (**alpha**) has been diversified away by having a sufficiently large portfolio, so that the expected return on the portfolio is a function of its beta alone.

Many academics challenge the use of variance in the formula for beta. They point out that variance is a symmetrical measure of risk, whereas investors are only concerned about loss (just the left side of the curve). Instead of variance, they point to other measures of risk, such as **coherent risks**, that may better reflect investor preferences. Coherent risks have four attributes:

1) When comparing two portfolios, the one with better values should have lower risk

2) The joint risk of two portfolios cannot exceed the sum of their individual risks

3) Increasing the size of positions within a portfolio increases its risk

4) Picture two identical portfolios except one contains additional cash. The one with the extra cash is less risky, to the exact extent of the extra cash.

Hedge funds clearly take on risks that are not reflected in beta. These risks are the basis for the returns of many strategies, such as long/short (liquidity risk), fixed income (credit risk), and sector trading (sector risk) to name a few. To the extent that a hedge fund takes on risks that are not reflected by beta, it is modifying its long-term expected return for better or worse. For instance, a portfolio may add an asset with a negative expected return in order to hedge another asset that has an expected positive return. This has the effect of lowering the expected return of the portfolio as it lowers the portfolio’s risk.

Recall that the expected market return above the risk-free rate is called the market’s **risk premium**. Many hedge funds seek returns independent of the market risk premium. Rather, hedge funds supposedly choose their risk exposures, and hence their risk premia. Ideally, their market beta would be zero, so that hedge fund returns would reflect only risks other than market risk. Note that these non-market risks are often hard to diversify away. For instance, it is difficult to diversify away the risks involved in “risk arbitrage” – a misnomer for the strategy of taking positions on mergers and acquisitions. By assuming this “event risk” (i.e. by betting on whether a proposed merger will succeed), fund managers hope to capture the associated risk premium, independent of market beta.

There are a large number of hedge fund strategies, and most are exposed to their own systematic risks. Later on, we will review different strategies in detail, and look at the associated risk premia at that time. *The important point here is that systematic risk, whether captured in market beta or due to strategy-specific risk(s), should not be conflated with *alpha* – the returns due to superior skill and/or timing.* Ultimately we will be exploring the case for and against alpha when we examine **hedge fund replication strategies**.

Next time, we’ll finish discussing the assumptions underlying CAPM.

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