Assymetric Payoffs

Investing is the interplay of hundreds and thousands of human interactions. Because human emotions and decisions are unpredictable, investment results are too, and don’t conform to the laws of mathematical probability (based on Gaussian statistics). For this reason, the most reliable estimate of risk is the worst case scenario loss. When evaluating a potential investment, it makes sense to review the potential gain, the potential  loss and the associated costs in order to determine the best opportunities. Estimating probabilities only inserts false precision.

Investment costs directly impact the expected return. Let’s suppose a very mediocre year in the markets, where stocks and bonds both return 3% over a 12 month period. Now suppose that an investor owned two mutual funds over the period, an equity (stock-market based) fund with annual costs of 2% and a fixed income (bond-market based) fund with annual costs of 1.5%. At the end of 12 months, after costs, the fixed income fund will have returned 1.5% net of fees (3%-1.5%), better than the equity fund which will have returned 1% net of fees (3%-2%). Fees and other costs exert a negative drag that reduces the expected return. Also, unlike market returns, fees are not only predictable, they are usually laid out beforehand. Reducing fees has a knowable and measurable positive outcome on investment results. However, while reducing costs makes sense most of the time, it is only one piece of the puzzle when determine expected outcomes. As an example, it doesn’t make sense to reduce fees at the same time as reducing expected outcome. As a simple example, the annual cost of a small cap fund or ETF is probably 0.5% higher than the cost of a large cap fund or ETF. However, the expected return for the small cap fund is probably at least 2% per year higher. While switching from small caps to large caps would make sense for reducing risk, it wouldn’t make sense if the only reason is to reduce fees. The mathematical expectation is -2% + 0.5% = -1.5%, meaning you would expect 1.5% lower returns each year, even though costs have been reduced.

Average returns, despite being commonly cited, don’t exist in market-based investments. One person explained it this way: If your head is in the oven and your feet are in the freezer, it’s fair to say that your average temperature is comfortable. True, but it’s the extremes that concern us here. The same is true with market investments. If the average return of two dissimilar investments is 8%, but one swings between -20% and +28% and the other swings between -1% and +17%, there is more chance of loss (in case of a forced liquidation) with the first investment. Again, it’s the extremes that concern us. Because of the nature of markets, my example is a little misleading. It’s not possible to know that an investment will swing between a minimum and maximum with any probability. Rather, We can only have an idea of potential outcomes. Let’s first look at potential losses. With an equity investment, the potential loss is 100%. If a company goes bankrupt or operations are discontinued for any reason, there is likely no equity to pay back investors. With a fixed income investment, the potential loss can range between 0% and 100%. In the case of an unsecured debenture, there is a chance of 100% loss. However, usually there are some assets available in the company, which may be liquidated to pay back investors. Some bonds are backed by specific assets which, if they hold their value, can guarantee a large portion of the investor’s capital. However, even government bonds are not completely safe. Many governments, including the US government and various provincial government in Canada, have reneged on debts owed, especially to their own citizens.

Relating the expected return to the potential loss gives and idea of the payoff characteristic of an investment. As an example, the potential return of an equity investment is unlimited (100% or greater) with a potential loss of equity (100%). The potential return of preferred shares (eg. trading at a discount) is the dividend yield (eg. 7%) + some capital gain (eg. 20%), depending on the trading price, while the potential loss is still 100%. The potential return and loss of a debenture is much the same as a preferred share. The potential return of a bond (eg. corporate) is the interest yield (eg. 5%) + a small capital gain (eg. 5%), while the potential loss depends on the assets providing the guarantee which may fluctuate in price (eg. 25%). Viewed in this way, preferred shares and debentures may be purchased for a valid reason (regular income), but they offer a worse gain/loss characteristic. This suggests two conclusions.

-First, investors should prefer asymmetric payoffs. The best investments are the ones that offer a higher potential gain with a lower potential loss. As an example, the common shares of a company with no debt and valuable assets has a lower potential loss than the common shares of a similar company with a high debt load. If the potential returns are the same (eg. the companies are the same size, in the same industry), it is clear that one offers a better expected outcome than the other. In fact, they may both provide the same return for a number of years, but in the case of a crisis or market crash, the safer company should produce a smaller loss and a higher chance of survival. And while equities present a variety of expected outcomes, preferred shares and debt appear less appealing, since there still exists the potential to lose capital, without providing a comparable return to equities. However, at least private debt offers assets which are bound to guarantee the debt, whereas public debt offers only the taxation power of the government, which could choose to reneg on their promise.

The ideal investment is one that offers an assymetric payoff. If the potential loss is smaller than the potential gain, the investment makes financial sense. In fact, it makes little sense to combine investments in a portfolio, if they all have a similar payoff (eg. unlimited loss and limited gain). A preferable approach is to combine assets with various assymetric payoffs, such as small cap equities (capital loss,  gains greater than 100%) with private debt of well-capitalised companies (small loss, small gains). I’m not suggesting that it’s possible to predict the level of gains available in small cap stocks, or that they need to generate huge returns to be profitable. This type of strategy has the best likelihood of preserving capital and generating gains, compared to a portfolio of stocks with uniform expected payoff characteristics (unlimited loss, limited gains), even if the (misleading) standard deviation and correlations imply a diversified portfolio. The test is not whether the portfolio performs adequately over a period of years, but whether or not it allows the investor to survive a market crash.


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