"When it comes to money, everybody is of the same religion." - Voltaire

Most people would agree that they want to make and have money, but very few people would agree to the level of risk they are willing to take on to make that money. Therefore, risk must be the first issue you address when you are looking at choosing your investments. (For more insight, see Determining Risk And The Risk Pyramid.)

Tutorial: Top Stock-Picking Strategies

In this article, we'll show you why the Sharpe ratio can help you determine which asset classes will deliver the highest returns while considering its risk.

The Sharpe ratio is designed to measure a unit of reward for each unit of risk taken. Let's take a look at this simple ratio in more detail.

Sharpe Ratio Dynamics
The Sharpe ratio, developed by Nobel Laureate William Sharpe, is designed to measure how many excess units of returns an investor can achieve over the risk-free rate for each unit of risk taken.

Thus, the Shape Ratio measures the risk/reward value of investors' assets class choices beyond the U.S. Treasury.

Let's take a look at the efficient frontier chart below to better illustrate the concept of risk, return and the Sharpe ratio.

Figure 1: Efficient Frontier - if you plot all the investment choices that you have at your disposal - stocks, bonds and portfolios of stocks and bonds, etc. - on the chart above, the resulting chart will be bounded by an upward sloping curve known as the efficient frontier.


Return Dynamics
Without taking on risk, you can achieve a level of return as indicated on the chart by the risk-free portfolio, the U.S. Treasury.

To achieve an additional X percent of return, you will need to take Z level of risk. Portfolio A represents your risk and return payoff. The Sharpe ratio of Portfolio A can simply be defined as X divided by Z. Portfolios B and C will deliver a higher level of returns should you choose to take additional risk beyond Z.

Unlike portfolio B and C, portfolios A' and A'' will deliver a higher level of returns for the same level of risk Z. Thus, A'' is preferable to A' and A' is preferable to A. The Sharpe ratio of A' is defined as X+Y divided by Z.

Therefore, the Sharpe ratio of A' is higher than that of A. Given the same level of risk Z, it can be concluded that any portfolio providing X plus additional returns should be considered superior. The additional achievable returns will be limited by the efficient frontier. Applying this same methodology, we can also presume that Portfolios B and C are superior if their Sharpe ratios are shown to be higher to that of A. (To learn more, check out Understanding The Sharpe Ratio and The Sharpe Ratio Can Oversimplify Risk.)

Breaking Down the Sharpe Ratio
A common mathematical definition of the Sharpe ratio for a portfolio is the excess returns of the portfolio over the risk-free rate divided by the portfolio's standard deviation.

Here is an illustration of the Sharpe ratio in the same efficient frontier chart:

Figure 2

It can be concluded that for a given level of risk (sp), Portfolio A can achieve a higher Sharpe ratio by following the blue arrow toward the efficient frontier or, for a given level of return (Rp), Portfolio A can also achieve higher Sharpe ratio by following the red arrow toward the efficient frontier.

Sharpe Ratio and Risk
The charts and the formula demonstrate that the Sharpe ratio penalizes the excess returns by adding of risk as defined by standard deviation. The standard deviation is also commonly referred to as the total risk. Mathematically, the square of standard deviation is the variance, Markowitz's definition of risk. (For further reading, see Understanding Volatility Measurements.)

So why did Sharpe choose the standard deviation to adjust excess returns for risk and why should we care? We know that Markowitz defined variance as something not to be desired by investors. Variance is defined as a measure of statistical dispersion or an indication of how far away it is from the expected value. The square root of variance, or standard deviation, has the same unit form as the data series being analyzed and is such more commonly used to measure risk.

The following example illustrates why investors should care about variance:

An investor has a choice of three portfolios, all with expected returns of 10% for the next 10 years. The average returns in the table below indicates the stated expectation. The returns achieved for the investment horizon is indicated by annualized returns, which takes compounding into account. As the data table and the chart clearly illustrates below, the standard deviation takes returns away from the expected return. If there is no risk, zero standard deviation, your returns will equal your expected returns.

Expected Average Returns
Year Portfolio A Portfolio B Portfolio C
Year 1 10.00% 9.00% 2.00%
Year 2 10.00% 15.00% -2.00%
Year 3 10.00% 23.00% 18.00%
Year 4 10.00% 10.00% 12.00%
Year 5 10.00% 11.00% 15.00%
Year 6 10.00% 8.00% 2.00%
Year 7 10.00% 7.00% 7.00%
Year 8 10.00% 6.00% 21.00%
Year 9 10.00% 6.00% 8.00%
Year 10 10.00% 5.00% 17.00%
Average Returns 10.00% 10.00% 10.00%
Annualized Returns 10.00% 9.88% 9.75%
Standard Deviation 0.00% 5.44% 7.80%
Figure 3

Figure 4

Conclusion
Risk and reward must be evaluated together when considering investment choices; this is focal point presented in modern portfolio theory. In a common definition of risk, the standard deviation or variance takes rewards away from the investor. As such, the risk must always be addressed along with the reward when you are looking to choose your investments. The Sharpe ratio can help you determine the investment choice that will deliver the highest returns while considering its risk.

To learn more, read Modern Portfolio Theory: An Overview.

Related Articles
  1. Mutual Funds & ETFs

    ETF Analysis: Direxion Small Cap Bull 3X

    Read about a triple-leveraged exchange-traded fund that aims for 300% of the returns of the Russell 2000 Index: the Direxion Small Cap Bull 3X.
  2. Fundamental Analysis

    Is India the Next Emerging Markets Superstar?

    With a shift towards manufacturing and services, India could be the next emerging market superstar. Here, we provide a detailed breakdown of its GDP.
  3. Mutual Funds & ETFs

    ETF Analysis: iShares MSCI USA Minimum Volatility

    Learn about the iShares MSCI USA Minimum Volatility exchange-traded fund, which invests in low-volatility equities traded on the U.S. stock market.
  4. Mutual Funds & ETFs

    ETF Analysis: iShares S&P Mid-Cap 400 Growth

    Learn about the iShares S&P Mid-Cap 400 Growth exchange-traded fund, which invests in U.S. equities of mid-cap companies that show above-average growth rates.
  5. Professionals

    Are Hedge Fund ETFs Suitable for Your Portfolio?

    Are hedge fund ETFs right for you? Here's what investors need to consider.
  6. Professionals

    Why Leveraged ETFs Are Not a Long-Term Bet

    Leveraged ETFs aren't for the average investor. They can, however, present significant upside potential for the right type of trader.
  7. Term

    Estimating with Subjective Probability

    Subjective probability is someone’s estimation that an event will occur.
  8. Investing Basics

    Understanding the Modigliani-Miller Theorem

    The Modigliani-Miller (M&M) theorem is used in financial and economic studies to analyze the value of a firm, such as a business or a corporation.
  9. Economics

    Explaining Kurtosis

    Kurtosis describes the distribution of data around an average.
  10. Personal Finance

    Simple Interest Loans: Do They Exist?

    Yes, they do. Here is what they are – and how to use them to your advantage.
RELATED TERMS
  1. Principal-Agent Problem

    The principal-agent problem develops when a principal creates ...
  2. Discount Bond

    A bond that is issued for less than its par (or face) value, ...
  3. Internal Rate Of Return - IRR

    A metric used in capital budgeting measuring the profitability ...
  4. Financial Singularity

    A financial singularity is the point at which investment decisions ...
  5. Revenue-based Financing

    Revenue-based financing, also known as royalty based financing, ...
  6. Precedent Transaction Analysis

    A valuation method in which the prices paid for similar companies ...
RELATED FAQS
  1. What is the utility function and how is it calculated?

    In economics, utility function is an important concept that measures preferences over a set of goods and services. Utility ... Read Full Answer >>
  2. What asset allocation should I use for my retirement portfolio?

    Asset allocation should be personalized to each individual investor's return objectives and risk tolerance. However, there ... Read Full Answer >>
  3. How does the risk of investing in the industrial sector compare to the broader market?

    There is increased risk when investing in the industrial sector compared to the broader market due to high debt loads and ... Read Full Answer >>
  4. What risks do I face when investing in the insurance sector?

    Like all equity investments, insurance companies present investors with market risk. Insurance companies, like banks, also ... Read Full Answer >>
  5. What are the main factors that impact share prices in the insurance sector?

    The main factors that impact share prices in the insurance sector are interest rates, earnings and actuarial risk. In the ... Read Full Answer >>
  6. How does the risk of investing in the retail sector compare to the broader market?

    The retail sector is divided into seven segments, all of which confer greater risk than the broader market. Retail securities ... Read Full Answer >>

You May Also Like

Trading Center
×

You are using adblocking software

Want access to all of Investopedia? Add us to your “whitelist”
so you'll never miss a feature!