Is Value Investing Rational? You Beta Believe It

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Previously, we examined the relative returns of value, growth and index mutual funds sold by Fidelity. While hardly scientific, it showed the growth fund badly trailing the other two. But this begs a larger question for value investors: why not just buy some low-fee index ETFs and go to sleep? You know your market risk in advance: index funds have a beta of 1.00. Beta is the relative volatility of a portfolio compared to that of the overall market. Index funds provide average risk and average returns.

Value investors’ strategy

The retort: value investors are looking to beat the market while reducing overall risk. An NYU study published in 2011 by Malcolm Baker et al gives support to the value investor’s strategy by showing that low-beta stocks, which are usually value stocks, outperform the market, Known as the low-risk anomaly, this finding flies in the face of the conventional Capital Asset Pricing Model (CAPM), which states that higher returns require higher risks. The study restricted its view to unleveraged investing — avoiding the use of margin or derivatives — which is a good proxy for open-end mutual funds, since they seldom use leveraging techniques. The results, in Baker’s own words:

Beta stock performance

Many investigators have commented on the low-risk anomaly, attributing several different mechanisms to its operation. The two main explanations for the underperformance of high-beta stocks are an irrational preference for high volatility and overconfidence, both of which cause investors to overpay. Baker’s contribution was to speculate on the role of index funds in helping to sustain the anomaly. The argument relies on some mathematics, but here is the gist:

  1. Irrational demand for high-beta stocks should provide an arbitrage opportunity in which other investors sell or short the high beta stocks and buy the low-beta ones.
  2. By regulation, every mutual fund must be benchmarked against a recognized index, such as the S&P 500.
  3. Benchmarking reduces a fund manager’s likelihood to arbitrage against overvalued stocks because of the CAPM relationship between risk and return:
    1. For low beta, high alpha stocks (alpha is excess return, equal to 1 – beta), the fund manager would not buy the stock unless its annual excess return exceeded alpha times the market return above the risk-free rate. Since many low-beta stocks would not clear this hurdle, the fund manager would be underweighted in these stocks.
    2. By similar argument, the fund manager would be overweighted in high-beta, low-alpha stocks.

See the article for a mathematical explanation, but the bottom line is that a fund manager has no incentive to buy and hold low-beta, i.e. value, stocks for the long term, because they don’t help him beat short-term benchmark returns and introduce risks that increase the tracking error between the fund and the benchmark. Baker suggests creating such an incentive by measuring performance against the Sharpe ratio rather than a benchmark.

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