For mutual funds Google Finance displays the following risk measurements (the first 5 are the more common technical risk ratios):
- Alpha*
- Beta*
- R-squared*
- Standard deviation
- Sharpe ratio
- Mean annual return
But what are the exact details of these metrics, how are they calculated, and what could you do with this information? I don't know really so I'll research them and note the salient bits of what I find for each here.
First off a general definition of risk from the investor perspective. Investopedia defines risk as "the chance that an investment's actual return will be different than expected. Risk includes the possibility of losing some or all of the original investment. Different versions of risk are usually measured by calculating the standard deviation of the historical returns or average returns of a specific investment. A high standard deviations indicates a high degree of risk." And they have a quick video on this at Investopedia: "Understanding Risk And Time Horizon."
Risk Measurement Points Explained
Alpha
From Wikipedia Alpha (investment): Alpha is a risk-adjusted measure of the so-called active return on an investment. It is the return in excess of the compensation for the risk borne, and thus commonly used to assess active managers' performances. It can be shown that in an efficient market, the expected value of the alpha coefficient is zero. Therefore the alpha coefficient indicates how an investment has performed after accounting for the risk it involved:
A positive alpha of 1.0 means the fund outperformed the benchmark by 1%, a negative alpha of 1.0 means the fund underperformed the benchmark by 1%. So the financial website Seeking Alpha states its goal clearly in its domain name.- αi < 0: the investment has earned too little for its risk (or, was too risky for the return)
- αi = 0: the investment has earned a return adequate for the risk taken
- αi > 0: the investment has a return in excess of the reward for the assumed risk
Beta
From Wikipedia the Beta (β) of a stock or portfolio is a number describing the relation of its returns with those of the financial market as a whole. An asset has a Beta of zero if its returns change independently of changes in the market's returns. A positive beta means that the asset's returns generally follow the market's returns, in the sense that they both tend to be above their respective averages together, or both tend to be below their respective averages together. A negative beta means that the asset's returns generally move opposite the market's returns: one will tend to be above its average when the other is below its average.
Published betas typically use a stock market index such as S&P 500 as a benchmark.
By definition, the market itself has a beta of 1.0, and individual stocks are ranked according to how much they deviate from the macro market. A stock whose returns vary more than the market's returns over time can have a beta whose absolute value is greater than 1.0. A stock whose returns vary less than the market's returns has a beta with an absolute value less than 1.0.
A stock with a beta of 2 has returns that change, on average, by twice the magnitude of the overall market's returns (i.e. when the market's return falls or rises by 3%, the stock's return will fall or rise by 6% on average). Beta can also be negative, meaning the stock's returns tend to move in the opposite direction of the market's returns. A stock with a beta of -3 would see its return decline 9% when the market's return goes up 3%, and would see its return climb 9% if the market's return falls by 3%.
Higher-beta stocks tend to be more volatile and therefore riskier, but provide the potential for higher returns. Lower-beta stocks pose less risk but generally offer lower returns.
Published betas typically use a stock market index such as S&P 500 as a benchmark.
By definition, the market itself has a beta of 1.0, and individual stocks are ranked according to how much they deviate from the macro market. A stock whose returns vary more than the market's returns over time can have a beta whose absolute value is greater than 1.0. A stock whose returns vary less than the market's returns has a beta with an absolute value less than 1.0.
A stock with a beta of 2 has returns that change, on average, by twice the magnitude of the overall market's returns (i.e. when the market's return falls or rises by 3%, the stock's return will fall or rise by 6% on average). Beta can also be negative, meaning the stock's returns tend to move in the opposite direction of the market's returns. A stock with a beta of -3 would see its return decline 9% when the market's return goes up 3%, and would see its return climb 9% if the market's return falls by 3%.
Higher-beta stocks tend to be more volatile and therefore riskier, but provide the potential for higher returns. Lower-beta stocks pose less risk but generally offer lower returns.
Relation between alpha and beta
An investor can use both alpha and beta to judge a manager's performance. If the manager has a high alpha and a high beta, an investor may not find that acceptable. This may be too risky for an investor who feel they might need to withdraw their money before a multi-year holding period. Thus investment managers who employ a strategy which is less likely to lose money in a particular year are often chosen by those investors who feel that they might need to withdraw their money sooner
R-squared
Investopedia explains 'R-Squared' as a statistical measure that represents the percentage of a fund or security's movements that can be explained by movements in a benchmark index. For fixed-income securities, the benchmark is the T-bill. For equities, the benchmark is the S&P 500.
R-squared values range from 0 to 100. An R-squared of 100 means that all movements of a security are completely explained by movements in the index. A high R-squared (between 85 and 100) indicates the fund's performance patterns have been in line with the index. A fund with a low R-squared (70 or less) doesn't act much like the index.
A higher R-squared value will indicate a more useful beta figure. For example, if a fund has an R-squared value of close to 100 but has a beta below 1, it is most likely offering higher risk-adjusted returns. A low R-squared means you should ignore the beta.
R-squared values range from 0 to 100. An R-squared of 100 means that all movements of a security are completely explained by movements in the index. A high R-squared (between 85 and 100) indicates the fund's performance patterns have been in line with the index. A fund with a low R-squared (70 or less) doesn't act much like the index.
A higher R-squared value will indicate a more useful beta figure. For example, if a fund has an R-squared value of close to 100 but has a beta below 1, it is most likely offering higher risk-adjusted returns. A low R-squared means you should ignore the beta.
Standard deviation
From the Yahoo! Risk Overview page the standard deviation is a statistical measure of the range of a fund's performance, and is reported as an annual number. When a fund has a high standard deviation, its range of performance has been very wide, indicating that there is a greater potential for volatility.
Approximately 68.3% of the time (2 of 3 occurrences), the total returns of any given fund are expected to differ from its mean total return by no more than plus or minus the standard deviation figure. About 95.4% of the time (19 of 20 occurrences), a fund's total returns should be within a range of plus or minus two times the standard deviation from its mean.
Standard deviation alone cannot be used to gauge risk. By only looking at the standard deviation one could conclude that a fund Y is more risky when compared to a fund X because Y has a higher standard deviation. But standard deviations by themselves are not necessarily a meaningful measure. To interpret risk you could divide the standard deviation by the average return and this could show fund X as more risky than fund Y depending on the avg return.
Approximately 68.3% of the time (2 of 3 occurrences), the total returns of any given fund are expected to differ from its mean total return by no more than plus or minus the standard deviation figure. About 95.4% of the time (19 of 20 occurrences), a fund's total returns should be within a range of plus or minus two times the standard deviation from its mean.
Standard deviation alone cannot be used to gauge risk. By only looking at the standard deviation one could conclude that a fund Y is more risky when compared to a fund X because Y has a higher standard deviation. But standard deviations by themselves are not necessarily a meaningful measure. To interpret risk you could divide the standard deviation by the average return and this could show fund X as more risky than fund Y depending on the avg return.
Sharpe ratio
Yahoo! Finance states the Sharpe ratio as a measure of a fund's excess return relative to the total variability of the fund's holdings. The higher the Sharpe ratio, the better the fund's historical risk-adjusted performance. It was developed by Nobel laureate William F. Sharpe to measure risk-adjusted performance. The Sharpe ratio is calculated by subtracting the risk free rate (i.e. 10-year U.S. Treasury bond) from the rate of return for a portfolio and dividing the result by the standard deviation of the portfolio returns.
A Sharpe ratio of 1 or better is considered good, 2 and better is very good, and 3 and better is considered excellent [Investopedia ref].
As it is a dimensionless ratio normal people (like me) will find it difficult to interpret Sharpe Ratios of different investments. For example, how much better is an investment with a Sharpe Ratio of 0.6 than one with a Sharpe Ratio of -0.1?
A Sharpe ratio of 1 or better is considered good, 2 and better is very good, and 3 and better is considered excellent [Investopedia ref].
As it is a dimensionless ratio normal people (like me) will find it difficult to interpret Sharpe Ratios of different investments. For example, how much better is an investment with a Sharpe Ratio of 0.6 than one with a Sharpe Ratio of -0.1?
Mean annual return
From Wikinvest the mean annual return
is the return an investment provides over a period of time, expressed
as a time-weighted annual percentage. Sources of returns can include
dividends, returns of capital and capital appreciation. The rate of
annual return is measured against the principal amount of the investment
and represents a geometric mean rather than a simple arithmetic mean.
Annual return is the de facto method for comparing the performance of investments with liquidity, which includes stocks, bonds, funds, commodities, and some types of derivatives.
US mutual funds use SEC form N-1A to report the average annual compounded rates of return for 1-year, 5-year and 10-year periods as the "average annual total return" for each fund. The following formula is used:
Both arithmetic and geometric average rates of returns are averages of periodic percentage returns. Neither will accurately translate to the actual dollar amounts gained or lost if percent gains are averaged with percent losses. A 10% loss on a $100 investment is a $10 loss, and a 10% gain on a $100 investment is a $10 gain. When percentage returns on investments are calculated, they are calculated for a period of time – not based on original investment dollars, but based on the dollars in the investment at the beginning and end of the period. So if an investment of $100 loses 10% in the first period, the investment amount is then $90. If the investment then gains 10% in the next period, the investment amount is $99.
A 10% gain followed by a 10% loss is a 1% loss. The order in which the loss and gain occurs does not affect the result. A 50% gain and a 50% loss is a 25% loss. An 80% gain plus an 80% loss is a 64% loss. To recover from a 50% loss, a 100% gain is required. The mathematics of this are beyond the scope of this article, but since investment returns are often published as "average returns", it is important to note that average returns do not always translate into dollar returns.
Annual return is the de facto method for comparing the performance of investments with liquidity, which includes stocks, bonds, funds, commodities, and some types of derivatives.
US mutual funds use SEC form N-1A to report the average annual compounded rates of return for 1-year, 5-year and 10-year periods as the "average annual total return" for each fund. The following formula is used:
P(1+T)n = ERV
Where:
P = a hypothetical initial payment of $1,000
T = average annual total return
n = number of years
ERV = ending redeemable value of a hypothetical $1,000 payment made at the beginning of the 1-, 5-, or 10-year periods at the end of the 1-, 5-, or 10-year periods (or fractional portion).
Both arithmetic and geometric average rates of returns are averages of periodic percentage returns. Neither will accurately translate to the actual dollar amounts gained or lost if percent gains are averaged with percent losses. A 10% loss on a $100 investment is a $10 loss, and a 10% gain on a $100 investment is a $10 gain. When percentage returns on investments are calculated, they are calculated for a period of time – not based on original investment dollars, but based on the dollars in the investment at the beginning and end of the period. So if an investment of $100 loses 10% in the first period, the investment amount is then $90. If the investment then gains 10% in the next period, the investment amount is $99.
A 10% gain followed by a 10% loss is a 1% loss. The order in which the loss and gain occurs does not affect the result. A 50% gain and a 50% loss is a 25% loss. An 80% gain plus an 80% loss is a 64% loss. To recover from a 50% loss, a 100% gain is required. The mathematics of this are beyond the scope of this article, but since investment returns are often published as "average returns", it is important to note that average returns do not always translate into dollar returns.
Concluding Comments
After researching these terms I feel better about knowing the specifics of these risk metrics and using them to some degree when I evaluate funds.
But I must say not quite sure what to make of standard deviation. How could or should it be utilized? What is considered a high standard deviation number? What is considered a low number? Is there an overall market average that I can compare a funds std dev against? Is the Google Finance reported standard deviation number a percentage? Is it OK to compare standard deviation across two different funds (i.e. a tech fund and a utility fund)?
From Wikipedia on the standard deviation there is this line: "Approximately 68.3% of the time (2 of 3 occurrences), the total returns of any given fund are expected to differ from its mean total return by no more than plus or minus the standard deviation figure."
Does this mean if a fund currently priced at $75/share and has a standard deviation of '5' (as reported on Google Finance) that I can say that share was between $95 and $105 per share ~66% of the time over the past 12 months?
As an example in the month of February 2012 let's compare MSFT and NFLX. Below is a chart comparing the two, red is NFLX:
Generally MSFT was at ~$30/share and NFLX ~$120/share over the month of February. MSFT had an up trend while NFLX had a downward trend. Just purely from my observations NFLX had much more volatility in February. According to MarketVolume MSFT had a 20-day Standard Deviation of 0.64. By comparison NFLX had a 20-day Standard Deviation of 5.61 So is NFLX nearly 10 times more risky than MSFT? NFLX was more volatile and therefore more risky but I don't think it was 10 times more risky, so what can I make of these reported standard deviation numbers? Also, can I compare this standard deviation number from MarketVolume to the number reported on Google Finance? Google Finance does not report a standard deviation for MSFT or NFLX. Is standard deviation only useful for mutual funds?
