Murphy’s Law and Risk

Many of us are familiar with Murphy’s Law from a negative connotation, this empirical principle finds its basis in the statement “If something can go wrong, it will probably go wrong.” Although this version is the most popular one, it is said that Edward Murphy never pronounced it as such.

A couple of years ago in Christopher Nolan’s “Interstellar”, Matthew McConaughey’s character (Cooper) refers to that law highlighting its neutral nature: “Murphy’s Law doesn’t mean something bad will happen, it means whatever can happen will happen.” And it is from this perspective that I would like to tackle a central issue in finance: risk.

In a broad sense, the term risk refers to the possibility of obtaining a different result than expected. For obvious reasons, it has always concerned us more when it differs negatively (associated with a loss) rather than when it manifests as an upside risk.

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The world of finance has designated the standard deviation as the measure of risk by convention. In statistics, the standard deviation is defined as a measure of the dispersion of data with respect to an average value. In other words, how different can a result be against what it is usually observed, or what would be expected frequently.

An application of the standard deviation could tell us how much the observed returns of an asset have deviated from its average over a given time horizon.

Following the idea that a higher return necessarily implies a greater degree of risk, as stated by Modern Portfolio Theory, we understand that the solution is not to eliminate it, but to optimize the combinations of assets that can lead to a higher return per unit of risk.

This time I would like to talk about a couple of tools that strongly support the proper risk management: diversification and time horizon.

Diversification

On the one hand, suppose we have two financial instruments, each with a certain associated risk and expected return. If the correlation between these two is not perfect — by perfect correlation meaning that a change in the variables yields a change in their outcomes in the same direction and magnitude — any combination will provide a higher expected return per unit of assumed risk.

In 5-year horizons the S&P 500 has posted a 7.4 compound annual growth rate from 1937 to date, with a standard deviation of 6.6 percent. If the market keeps up with this performance, let’s see how its expected performance and risk scenarios would be if we combine it with a risk-free instrument such as the US 10-year bond, which today would yield a return of 2.31 percent.

In our simulation, a portfolio with a 100% exposure to equities would have an expected return of 7.4 percent, with an optimistic scenario of 20.5 and a pessimistic one of -5.7 percent in a one year time span. As the weight in equities is reduced — thus increasing our stake in the risk-free asset — the pessimistic scenario shrinks to -0.1 percent when there is a 30 percent share in equity and 70 percent in risk free assets. In this scenario, the base case shrinks to 3.8 percent, as well as the optimistic, which reaches 7.8 percent. “To choose is to resign.”

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Time horizon

Our other great ally to reduce risk is the time horizon. In our analysis of the S&P 500, for the last 80 years, we have seen how, in sufficiently large time spans, the probability of incurring a loss is reduced.

As such, while temporal losses might be experienced, markets’ and economic cycles, along with the value of the compound interest, ultimately yield positive results for patient investors.

At 10-year intervals, the largest fall recorded is a compound annual loss of 6.2 percent, despite not being a negligible one, if we extend the scenario to 15-year spans, the lowest result yields a compound annual return +0.5 percent (+7.90 percent effective) and in 20 years a compound annual return of +2.1 percent (+52.9 percent effective).

Although the basis of this exercise takes for granted certain assumptions, such as normal distribution of returns, and it is based on historical behavior, the fact is that consistency in results should grant comfort to the long-term investor.

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Source: Bloomberg with data for the S&P from October 1937 to 2017.

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