How Hollywood, lotteries and mutual funds show that all risk is relative

One of the great ironies in the hedge fund industry is the propensity for many investors to favor relative returns over absolute returns. This is particularly true among retail investors who, by and large, would prefer to lose money along with everyone else than to make less than everyone else. What else could explain the complacency with which investors accept -40% market returns while crying foul at the hedge funds that “under perform” in a bull market.

Research into happiness has dispelled the notion that utility is derived from some absolute level of wealth. Instead, it appears that utility is relative, not absolute - hence the paradox of the retail investor who is petrified of under performing his neighbours, but sanguine about losing his shirt alongside them.

More than some esoteric argument, the phenomenon of relative wealth may actually account for the overwhelming amount of empirical evidence than seems to refute the hallowed Capital Asset Pricing Model. In a paper released last month based on his new book “Finding Alpha“, author Erik Falkenstein argues that:

“The standard assumption that relevant volatility is absolute wealth may be a good normative theory, but a relative wealth orientation generates a more accurate positive theory, and its assumption is generally considered more accurate by those doing research on the essence of subjective well-being..The relative status utility function generates a more accurate description of the world..”

Falkenstein delivers a litany of empirical evidence suggesting that risk and reward are negatively correlated across many asset classes, not positively correlated as the CAPM proposes.

He begins by citing his own 1994 Ph.D. thesis showing how mutual funds with higher idiosyncratic risk actually have a lower annual excess return than those with low idiosyncratic risk.

He then cites research proving that portfolios of high-beta stocks have a lower Sharpe ratio than portfolios of low-beta stocks. In other words, the Security Market Line is downward sloped, not upward sloped (see related post). He shows a similarly negative relationship between risk and return of call options.

But the most interesting part of this paper is Falkenstein’s exploration of non-traditional asset classes. For example, he cites the private equity industry as further proof that the risk and reward are negatively correlated. Research cited in the chart below show that (high risk) privately-owned businesses produce returns that are pretty much the same as a (low risk) diversified public equity portfolio:

As Falkensetin observes:

“Given an investor can invest in a diversified, and liquid equity portfolio, it is puzzling why households willingly invest substantial amounts in an asset with an equivalent return, but much higher volatility, including a positive correlation with the market…Entrepreneurs appear to be taking extra risk, for no extra return.”

The list of so-called CAPM “anomalies” continues with evidence that leveraged companies have lower returns and how the success (until recently) of the carry trade is further proof that risk and reward are not significantly correlated after all.

Even the equity premium in different countries seems to refute the CAPM. As the chart below from the paper shows, there is little relationship between the equity premia and returns in 17 countries:

One of the more “alternative” examples of a CAPM transgression presented by Falkenstein is from Hollywood. He cites research showing that “R” rated movies generated the same average gross returns than “G” rated movies, but with a risk that was nearly 20 time higher.

In other words:

“It seems studio executives are generally betting on the next Titanic, because the very highest grossing movies are R rated.”

Horse betting (where 1-10 odds produce higher returns than 100-1 odds over the long run) and lotteries (which have a -47% return per dollar played) are further proof that “investors” are willing to accept lower long-term returns in exchange for the opportunity to hit the jackpot. (ed: So much for my plan to start a hedge fund that invests in lottery tickets). As Falkenstein observes:

“People who buy lottery tickets seem to prefer those lotteries that offer the worst odds, but the greatest payout.”

In an effort to put these anomalies into formula, Falkenstein presents a simple example showing that absolute risk aversion may be asymmetrical, but that relative risk aversion can still be symmetrical.

For the hedge fund (”absolute return”) industry, the message is familiar: investors may be more concerned about the political and reputational risk of underperformed their peers than they are about the absolute risk to their portfolios - or, as Falkenstein puts it:

“Risk is simply allocating an “unusual” amount of wealth to any asset that would generate a significant deviation from the market portfolio.”