27 Feb 2016

Measuring Risk with Investments

When you invest, you have to choose between various options, and one important factor in this decision is how much risk an investment entails [1].

But how do you measure risk? The usual metric is standard deviation. But it suffers from many problems, the most important of which is that it’s hard to apply practically. If I tell you that your fund’s standard deviation is 14, how much of a fall in value can you expect if the market goes down? Most people wouldn’t be able to answer that question because of the esoteric manner in which it’s defined. Even people like me who are mathematically inclined but are not statistics geeks have a hard time relating this number to real life. It’s as useful as saying that the compression ratio in your car engine is 16:1. Metrics that you can’t draw useful conclusions from are useless to you [2].

There are other, even more esoteric metrics like beta and R-squared. Needless to say, these are even more useless to everyday investors.

I can think of two metrics that are easier to relate to our intuitive understanding of risk, easy to calculate, and easy to apply. One is suitable for a long-term investment, and the other for a short-term investment.

Measuring risk for a long-term investment

For a long-term investment, risk is  the shortest period of time you have to stay invested to avoid a loss. Equivalently, what’s the longest period over which an investor lost money?

When you make a long-term investment, you shouldn’t care about temporary fluctuations, even if they are many, or deep, provided your investment recovers. By this measure, the Sensex has had a period of 15 years where investors lost money [3].

Debt is considered safer, but how much safer? A debt fund with high returns and high risk (Franklin Income Builder) has never lost money over a one-year period [4]. So, the answer is that this debt fund was 15 times as safe as the Sensex.

The safest debt funds are liquid funds, which have had only a two-week period with no returns. FDs are even safer, with no period of negative return. They were absolutely safe by this metric [5].

There are many variations of this question you can ask. Instead of asking what the shortest time was that you had to stay invested in to avoid a capital loss, you can ask what the shortest time was to keep pace with inflation. After all, if your investment has had a 0% return, you’ve lost value to inflation. By that measure, the Sensex required you to stay invested [6] for 15 years to generate a positive real return.

Or you can ask what the shortest period of time was that you have to stay invested for for your equity investment to generate a higher return than debt. In the US, for example, there has been a 30-year period in which debt outperformed equity [7] [8].

These are all forms of the question, “What’s the shortest period of time you had to stay invested in for <X>?”

Or, since you’re a long-term investor, you can ignore time periods shorter than a decade, and ask, “What’s the probability of a 10-year investor losing money?”

Measuring risk for a short-term investment

Not all investments are long-term. You may invest money for a goal next year, like ₹6 lac to buy a car. Or you may have an emergency fund that you need to draw upon at any time.

For such short-term investments, it’s better to define risk as the greatest capital loss that has ever occurred in the investment over any period of time. This is the biggest peak-to-trough fall. It captures the experience of an investor who has had the misfortune to invest at exactly the wrong time, and then redeemed their investment at exactly the wrong time [9].

The stock market has had a 64% fall when the 2008 financial crisis struck. The aforementioned Franklin Income Builder debt fund fell only 8%. And liquid funds fell only 0.4%.

These two measures of risk are more useful than esoteric ones like standard deviation. They correspond to your intuitive definition of risk, you can easily calculate them, and you can easily apply them to make a decision.

[1] Needless to say, the reason you take risk is to earn higher returns.

[2] There are also theoretic problems with standard deviation. To begin with, it assumes a normal distribution, which is questionable.

Then, standard deviation is affected by upside risk. An investment whose
returns fluctuate between 5% and 10% is considered riskier than one that
always returns 5%. This makes no sense. There’s zero risk in the

[3] Including dividends.

[4] These are not perfectly comparable since they are for different time periods.

[5] Ignoring other factors like suspension of redemptions.

[6] Notice the pervasive use of the past tense.  Needless to say, past performance is no guarantee of the future.

[7] Over the 30 years from 1982 through 2011, long-term Treasury bonds returned 11.03 percent annually on average, slightly eclipsing the S&P 500, which returned 10.98 percent including dividends.

[8] Using the stock market index as a proxy for equity returns.

[9] This captures the experience of naive investors, who invest when at the peak of the market, when everyone is talking about the amazing returns their uncle has made. And then a crash happens, and these people as the market falls and falls and eventually they can’t wait anymore and they sell at or near the trough. A friend of mine made this mistake. This is unfortunate, but on the other hand, people like him increase my returns as a long-term investor who can buy near the trough :)

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