How We Define Risk – the Keppler Ratio

Controlling risk is the main focus of our investment strategies and the secret behind their success. Having long rejected the notion that portfolio risk is strictly a function of the volatility of portfolio returns, we define risk as expectation of loss – a measure that focuses on the probability and magnitude of investment losses rather than the variability of returns. In calculating risk–adjusted returns, we consequently do not apply the Sharpe Ratio, which indicates return per unit of variability, but the Keppler Ratio – a risk–adjusted performance measure first proposed by Michael Keppler in 1990 (see Publications section of this website). The Keppler Ratio indicates the return per unit of expectation of loss. We consider this ratio a more meaningful measure of risk–adjusted performance because losses (which can be defined as negative returns or as negative deviations from the required rate of return) are what most investors intuitively perceive as risk. Volatility measures, on the other hand, proposed as risk proxies by the proponents of modern portfolio theory and widely used by fund rating agencies to evaluate investment managers and mutual funds, do not distinguish between upside and downside price movements and can lead to questionable risk assessments.

Why Risk Management Is Critical to Successful Investing

Managing risk as we define it means striving to minimize the probability and size of investment losses. Warren Buffett is famous for saying that the first rule of investing is “Don't lose money” and the second rule is “Never forget the first rule.” The chart below reveals the wisdom behind this facetious overstatement and underscores the importance of controlling the risk of loss. If an investor loses 10 %, the gain required to recover from this loss is not 10, but 11.1 %. As losses increase, it becomes ever more difficult to break even. To recover from a 33.3 % loss, one needs a 50 % gain, and a 100 % gain is required to erase a 50 % loss. The reason for this phenomenon is that returns are connected geometrically rather than arithmetically, and the return required to compensate for a previous loss increases hyperbolically.

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How We Manage Risk

The Capital Asset Pricing Model, one of the central paradigms of financial economics, assumes a positive linear relationship between portfolio risk (defined as volatility in relation to the market) and portfolio return. Risk, according to this theory, is the price of reward, and reward is proportional to risk. If this were true and the returns investors can expect to achieve were strictly dependent on the risk they are willing to assume, it would be impossible to reduce risk without sacrificing potential returns.

This assumption may be correct in the short term. An investor faced with imminent liquidity needs may well be forced to forgo investment opportunities that offer the potential of high long–term returns at high short–term risk. However, our extensive research on global equities and the long–term track record of our portfolio strategies suggest that, by focusing on value, long–term investors are able to not only manage risks effectively but also to achieve superior returns. Stocks bought with an adequate margin of safety offer both extra downside protection and enhanced upside potential, which tends to be realized over time, as the gap between price and value closes. In the long run, the most defensive investment strategies are the ones that also promise the richest rewards. Yet, blinkered by a focus on the short term and driven by a demand for instant gratification, many investors attempt to manage risk through market–timing and hedging strategies that are often dangerous to their long–term wealth. Transaction costs, taxes and lost upside potential usually outweigh any reduction in the short–term risk of loss they may achieve by speculating on the direction of future price moves.

We believe that a margin–of–safety approach to managing risk is a far more powerful and reliable way of controlling portfolio losses without limiting potential returns. Diversification across markets, sectors and stocks is another important component of our portfolio strategy and further contributes to risk reduction. Given the time–dependent nature of risk, we advocate long holding periods to enable investors to realize the long–term benefits of prudent portfolio construction and diversification. A long–term outlook also allows them to take full advantage of the power of compounding.

If risk, in the last analysis, is a function of price and time, and controlling risk is the key to achieving superior returns in the global equity markets, the prescription for investment success can be condensed to the following simple formula: “Don't overpay, and invest for the long term!”