Risk vs. Return

How to compare asset allocations using risk and return measures

Investment risk is the likelihood that your investment will perform poorly. This could mean that your portfolio suffers a loss, or that your portfolio does not perform as well as you expect.

Because no one can perfectly predict the future, we can estimate a portfolio's risk using several different historical measures to predict future risk.

Risk is usually stated as a percentage over a time period such as "15% per year." The risk characterized by the percentage depends on the risk measure being used. For example, one risk metric could measure the maximum percentage loss that a portfolio has suffered over the past 10 years. Another risk metric could average the monthly declines in a portfolio over the course of a year.

How do we measure risk?

Below are several popular ways to measure risk.

Standard deviation. This measures how a portfolio's returns compare to the portfolio's longer-term annual average return.

Examples:

• A portfolio that consistently returned 5% per year for four years has a standard deviation of 0.0%.
• A portfolio returning +5%, then 10%, then -10%, then -5% has a standard deviation of 9.1%
• A portfolio returning +4%, then 5%, then 6%, then 5% has a standard deviation of 0.8%

U.S. Stocks typically have a standard deviation between 15% and 20%

U.S. Investment grade bonds typically have a standard deviation between 5% and 10%

Maximum drawdown. This measures the largest decrease in a portfolio's value, from peak to trough. This should be considered over a period of at least 7 years that contains an overall market drop. If you just look at maximum drawdown over a period when assets are rising, you will get a small percentage and this will not be useful for determining the risk of the portfolio during a downturn.

Examples:

• A portfolio consistenly returned 5% per year for four years. Its maximum drawdown is 0%.
• A portfolio returned +5%, then 10%, then -10%, then -5%, Its maximum drawdown would be 14.5%
• A portfolio returned +4%, then 5%, then 6%, then 5%, its standard deviation would be 0%, since there were no losses during the period.

Downside deviation. This measures how a portfolio's negative returns compare to the portfolio's longer-term average of negative returns. This is similar to standard deviation, execept that only negative returns are considered. The reasoning behind this is to avoid penalizing a portfolio for its positive returns.

Beta. This measures how much a portfolio's return varies compared to a benchmark. The benchmark is typically an index of stocks, such as the S&P 500. A beta of 1.0 means that a portfolio's returns will typically track the underlying index. A beta of 1.1 means that the portfolio will typically vary 1.1% for every 1.0% change in the benchmark.

How do we measure return?

A portfolio's return is its increase in value from year to year. For example, if a portfolio has a value of \$10,000 on Dec 31, 2014 and a value of \$11,200 on Dec 31, 2015, then the one-year annual return is 12.0%. When measuring return over more than one year, there are different methods to calculate the average or aggregate return.

Two popular ways to measure return are as follows:

Average return. This simply takes the average (arithmetic mean) of all the returns in the time period.

Examples:

• A portfolio that consistently returned +5% per year for four years has an average return of 5.0%.
• A portfolio returning +5%, then +10%, then -10%, then -5% has an average return of 0.0%
• A portfolio returning +10%, then +20%, then +10%, then +20% has a standard deviation of 15.0%

Compound annual growth rate. This is also called CAGR or compound return or year-over-year growth rate. This method assumes that you reinvest your returns from the prior year. The CAGR shows the return that you needed each year over a given time period to produce the same results as if your portfolio had reinvested the actual annual return each year.

Examples:

• A portfolio that consistently returned +5% per year for four years has a CAGR of 5.0%.
• A portfolio returning +5%, then +10%, then -10%, then -5% has CAGR of -0.3%
• A portfolio returning +10%, then +20%, then +10%, then +20% has a CAGR of 14.9%

Note that returns calculations can be very sensistive to the time period chosen. For example, if you see a 5-year return of 12% per year that sounds nice until you realize that 7 years ago the portfolio fell in value 50%. The 7-year return for that same portfolio would be much lower than 15% per year.

How do we compare Risk vs. Return?

One way to combine risk and return is by using a "risk-adjusted return" or a score which includes risk and return measures.

Also several companies provide Ratings & Scores comparing % risk and % return for a portfolio and then generating a single number or score for each portfolio.

Below are several ways to measure return vs. return using a single number or value.

Alpha (or Jensen's alpha). This percentage shows the extra return that a portfolio generated, above the expected return, while accounting for the portfolio's volatility. The expected return is usually set as a broad market index such as the S&P 500.

Sharpe ratio. This is a unitless ratio of % return to % risk, so a higher Sharpe ratio is better. Return is defined as the excess return over a benchmark, where the benchmark is a riskless investment such as a Treasury bill or cash equivalent. The risk measure is standard deviation. This measure was first described by William Sharpe in 1956.

VizMetrics V-Score. This is a risk-adjusted scoring system that rates each portfolio from 0 to 100. A score of 100 is best and zero is worst. A score of 100 means that a portfolio has outperformed an optimal global portfolio which uses 14 global asset classes. A score of zero means that a portfolio has done worse than the worst of the 14 asset classes.

Morningstar Star Rating. This is a scoring system that rates each portfolio from 5 stars (highest) to 1 star (lowest). The star ratings are assigned within specific peer categories (e.g., international portfolios, stock portfolios, bond portfolios, etc.) so it's possible for a lower-performing porfolio to get a high star rating, as long as it is better than the other portfolios in its category.

Lipper Leaders. This is a scoring system that rates each portfolio from 5 (highest) to 1 (lowest). The ratings are based on peer groups, similar to the Morningstar Star Rating system.

Modigliani-Modigliani (or M-squared). M-squared is a risk-adjusted performance measure, shown as an annual total return %. It is derived from the Sharpe ratio, but M-squared is in units of percent return. Since M-squared is shown in units of percent, this measure can be easier to understand than the unitless Sharpe ratio. M-squared inputs include standard deviation, the monthly total return, the risk-free rate (such as the 3-month T-bill rate), and the return of a benchmark portfolio (such as the S&P 500). This measure was first described by Nobel Prize winner Franco Modigliani and his granddaughter Leah Modigliani.

Treynor ratio (or reward-to-volatility or Treynor measure). This is unitless ratio compares return and risk. Return is defined as the excess return over a benchmark, where the benchmark is a riskless investment such as a Treasury bill or cash equivalent. The risk measure is beta. This measure was first described by Jack Treynor.

Sortino ratio. This is a unitless ratio compares return and risk. Return is defined as the excess return over a minimum acceptable return. The minimum acceptable return can be set to 0%, or to the risk-free (cash) return rate, or some other "hurdle rate." The risk measure is downside deviation. This measure was first described by Frank Sortino.