Measuring the Risk and Return Tradeoff

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 Peter Lazaroff By: Peter Lazaroff

In an earlier post, we started the process of defining risk by introducing three key ideas:

  1. Given the choice of two portfolios with identical returns, we should prefer the one with the lowest amount of risk.
  2. The word “risk” is used to describe the volatility of returns, which we quantify using standard deviation.
  3. The higher the standard deviation, the more volatile (risky) the investment is expected to be. We could also say that a higher standard deviation means there is a more uncertainty in our expected return.

These three main points were demonstrated by comparing two portfolios with the same average return, but different levels of volatility. The problem with this analysis is that it doesn’t apply well to real life in which investors must compare multiple portfolios with different returns.

In order to make an apples-to-apples comparison, we must make an adjustment for risk using the Sharpe Ratio. The technical description of the Sharpe Ratio is it allows us to measure risk-adjusted returns, or the amount of additional return per unit of risk.

Use the Sharpe Ratio to Better Understand the Concept of Risk Return Trade Off

In simpler terms, the Sharpe Ratio is a useful way to gauge the risk return tradeoff. The higher the Sharpe Ratio, the better the risk return tradeoff. This is useful because one portfolio may be able to achieve higher returns, but it is only a good investment if the higher returns don’t come with too much additional risk.

Risk Return Tradeoff in Financial Management

Let’s look at an example. Below we have the Sharpe Ratio equation followed by a table showing four funds with different returns and standard deviations. In this example, we use the Sharpe Ratio to identify the fund with the best risk-adjusted returns:
Sharp Ratio for Risk Return Trade Off

Fund A and Fund B have identical returns, so we know to choose the fund with the lower volatility, which is Fund B. We would expect Fund B to have a higher Sharpe Ratio because it earns a higher return and has lower volatility (standard deviation). Fund B has a higher risk-adjusted return and, thus, is the preferred over Fund A.

Now let’s compare Fund B and Fund C. Fund C offers a higher return than Fund B, but it is also more volatile. This is the perfect scenario to use the Sharpe Ratio. Remember: a higher Sharpe Ratio is better and indicates higher risk-adjusted returns. Fund B has a Sharpe Ratio of 1.25 and Fund C has a Sharpe Ratio of 1.40, which means that Fund C earns a higher risk-adjusted return than Fund B.

Finally, Fund D has the highest return and the highest volatility of the four options. Using the Sharpe Ratio, we can see that Fund D has a higher risk-adjusted return than Fund A and Fund B; however, the compensation for taking on additional risk assumed in Fund D is not as great as Fund C. The Sharpe Ratio indicates that Fund C offers the highest risk-adjusted return and is the best investment option.

The Sharpe Ratio is one of the many tools we use internally to evaluate investment funds, strategies, and assets classes in client portfolios. A variation of the above ratio is to use a different Benchmark Portfolio, such as an index (e.g. S&P 500, Russell 2000, MSCI EAFE, etc) instead of the risk-free rate.

However, this is less useful when comparing investments across different asset classes. Another related tool we can use is the Sortino Ratio, which focuses specifically on downside volatility.

To summarize, we started our discussion of risk by explaining that an investor should select the least risky portfolio when choosing between portfolios with identical returns. Given that it is rare for all portfolios to have the exact same returns, our goal is to generate the best risk-adjusted return. Volatility is the cost of higher returns and the Sharpe Ratio helps us ensure we get the most bang for our buck.

The next piece of the puzzle is understanding your personal risk tolerance. Even if a high-risk investment earns a sufficient amount of return to justify the volatility, some investors are unable or unwilling to take such risk. Our objective at Plancorp is to create a portfolio with an amount of risk that generates sufficient profit, but still allows you to sleep at night.

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Disclosure:

This material has been prepared for informational purposes only and should not be used as investment, tax, legal or accounting advice. All investing involves risk. Past performance is no guarantee of future results. Diversification does not ensure a profit or guarantee against a loss. You should consult your own tax, legal and accounting advisors.

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Peter Lazaroff, Chief Investment Officer, first took an interest in investing when his grandmother gave him a single share of Nike stock for his 13th birthday. Today, nearly 20 years later, his investment insights are highly sought after by local and national media. More »