Gain and Loss as Key Elements to Describing an Investment Opportunity
Most economists would agree that gain and loss are key elements to describe an investment opportunity. The ex-ante perceptions of potential gain and loss not only determine the attractiveness of an investment opportunity but they are also relevant for its relative valuation given the investor’s risk attitude. Investors generally have a reference rate of return below which they would feel disappointed by their investment outcome. Downside risk captures scenarios in which the actual investment return falls below the investor’s reference rate of return.
There are two key measures when considering downside risk: the probability of experiencing a loss, that’s the frequency of losses, and the size of the average loss, that’s the amplitude of losses. Think of the difference between AM radio and FM radio. AM radio works by modulating the amplitude of the signal, while FM radio works by modulating the frequency of the signal. This is almost how investors with aversion to downside risk typically make investment choices. That is, they try to modulate the amplitude and the frequency of their losses. It’s all about losing often but little amounts versus losing big but in rare cases.
Ideally, investors would look for investments that offer a small probability of small losses, combined with a very high probability of large gains. But that sounds like a free lunch. This would typically not happen in well-functioning financial markets! If we are looking for situations in which the probability of losing is small, then it is reasonable to assume that the size of that loss might be large. Conversely, if the probability of losing is big, then we can cautiously assume that the size of the loss will be small. Aversion to downside risk is thus characterized by two types of investment choices: low-frequency large losses and high-frequency small losses. Which of these two types is relevant for an investor depends on the reference rate of return.
Bond Investors vs. Stock Investors
Investments with low-frequency but large losses generally go hand-in-hand with frequent but small gains. In other words, the revenue is steady and the probability of losing is low, but if you do lose, you lose big. Selling insurance is an artificial example of such investments. They attract investors who like to win often, just like bond investors who are looking for steady income and do not expect to make sizeable gains.
Likewise, investments with frequent but small losses go hand-in-hand with low-frequency but large gains. The probability of losing is big, but if you do lose, you lose small. Buying lottery tickets is an artificial example of such investments. They attract investors who like to win big, like stock investors who are looking for big returns and should not expect those returns to be recurrent.
What Does Current Research Have To Say?
In the academic research, standard portfolio choice models do not assume downside risk in investment outcomes; neither do they consider investor’s aversion to downside risk. In consequence, these settings prove unsuccessful in explaining important facts observed in the asset management industry. Downside risk and aversion to it, as assumed in recent advances in portfolio choice research can rationalize various forms of equity investing. At the same time, it explains actual portfolio recommendations by popular financial advisers such as Fidelity Investments, Merrill Lynch, and The New York Times. Finally, it is shown that the welfare costs of ignoring downside risk and investor’s aversion to it can be large.