We always assume that better returns mean a good investment. But too risky investments can produce good returns too and you may fall for such investments. It is better to go for an investment which gives good returns but for optimal risk. But how can you differentiate between such investments? In such cases Sharpe ratio can be useful; as it helps you choose an investment which generates higher return for optimal risk taken.

Take a high-risk investment for example. This investment is much more volatile, increasing and decreasing in value much more, than a low-risk investment. Assume that the high-risk investment had a higher return than the lower investment for a given year. Was this because the high-risk management or investment outperformed the low-risk investment or is this higher return simply based on the higher risk and volatility of the high-risk investment? We would never be able to know without this ratio.

#### Definition: Sharpe Ratio

- The Sharpe ratio is an investment measurement that is used to calculate the average return beyond the risk free rate of volatility per unit. In other words, it’s a calculation that measures the actual return of an investment adjusted for the riskiness of the investment.
- Sharpe ratio is a single figure which shows how much is the risk adjusted return a fund can offer. It would tell you whether higher return is due to additional risk or better decisions of the fund manager.
- It is the average returns generated over and above the returns a risk free investment generates per unit of risk.
- Risk in this case is standard deviation. Standard deviation which comes in the denominator, gives the volatility of the returns.
- This measurement is particularly important when comparing two or more investment opportunities because it levels out the volatility in the market and flattens out the returns as if the risk was eliminated.

#### Formula

- The Nobel laureate, William F. Sharpe, created the Sharp Ratio as a way to cancel out the risk component of investing in an effort to compare two different investment returns. Let’s see how to calculate the Sharpe Ratio. Mathematically, it is represented as,
- Sharpe ratio = [ Average Returns of a portfolio – Returns of a risk free investment ] / Standard deviation of the portfolio
- Sharpe Ratio = [ Rx – Rf ] / Std Dev
- Where,
- x = the investment
- Rx = Average return of the investment
- Rf = Returns of a risk free investment
- Std Dev = Standard Deviation of the return

- We are basically subtracting the risk free rate of return from the mean return to isolate the return based on the level of risk. We can then evaluate the investment performance based on the risk-free return.
- Basically, the Sharpe ratio equation adjusts portfolios for risk and puts them all on a level risk playing field, so they can all be compared equally.

#### example

- From the above figure, we can see that Investment B out performed investment A by a rate of 50% [ 30% = 1.5 * 20% ], but this doesn’t mean that investment B performed well relative to its risk level.
- The sharpe ratio tells us that the first investment A actually performed better than the second investment B relative to the risk involved in the investment. If the second investment performed as well as the first investment relative to risk, it would have earned a return of 90 percent.
- The second investment may have earned a higher return this year, but it has a higher risk and likelihood of volatility in the future.

#### What does sharpe ratio reveals?

- A higher Sharpe ratio indicates a higher return generated per unit of risk taken.
- A higher Sharpe metric is always better than a lower one because a higher ratio indicates that the portfolio is making better investment decisions.
- Subtracting returns of a risk free investment from average returns, we get returns generated by taking risk, which makes comparison of funds within the same category simple.
- Returns offered by FD, government bonds, etc. can be taken as ‘returns of a risk free investment’ for calculation purpose. The belief here is that government securities, FD etc. do not involve any risk taking. Sharpe ratio tells you if the returns from the investments are due to good decisions or due to unnecessary risk taken.

- <1: Not Good
- 1 – 1.99: Ok
- 2 – 2.99: Really Good
- >3: Exceptional

- Take a portfolio that only invests in Treasure bills for example. These are considered risk-free investments, so there is no volatility and no earnings in excess of the risk-free rate. Thus, the Sharp Ratio would be zero for this portfolio.
- Other portfolios with higher rates of risk might have a metric of 1, 2, or 3. Any metric equal to or greater than 3 is considered a great Sharpe measurement and a good investment all else equal.
- A metric of 1, 2, or 3 tells us how much additional return we are getting for holding an risky investment over a risk-free investment. In a sense, it shows us the level of compensation we are receiving for the additional level of risk we are taking with the investment.

#### How to use sharpe ratio?

- Sharpe ratio is a number and is useful only when used to compare funds or compare a fund with its bench mark.
- Fund managers use this ratio to check whether adding an asset does any good to the portfolio.
- Investors use the equation to see if they are comfortable with a particular investment. For example, they might feel that the return isn’t high enough for a certain level of volatility.
- The higher the Sharpe ratio the better it is. But beware as this could be misleading if a fund has lower standard deviation. So, again, we should read Sharpe ratio with other parameters like Alpha, Beta, Standard deviation, etc. to get a clear picture of the returns generated.

#### summary

- The Sharpe ratio is an investment measurement that is used to calculate the average return beyond the risk free rate of volatility per unit. In other words, it’s a calculation that measures the actual return of an investment adjusted for the riskiness of the investment.
- This measurement is particularly important when comparing two or more investment opportunities because it levels out the volatility in the market and flattens out the returns as if the risk was eliminated.
- A higher Sharpe ratio indicates a higher return generated per unit of risk taken.

A higher Sharpe metric is always better than a lower one because a higher ratio indicates that the portfolio is making better investment decisions.

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