Mutual Fund Beta, Standard Deviation, and Sharpe Ratio
As we know, risk measures include various attributes such as –
● Beta
● Alpha
● Standard Deviation
● Sharpe Ratio
We will start with the beta.
One of the most important characteristics of the mutual fund is its beta. The beta of a mutual fund is a numerical representation of the fund's relative risk; Beta can take any value above or below zero. Beta provides insight into the relative risk of the mutual fund relative to its benchmark.
If a mutual fund's beta is smaller than 1, the fund is deemed to be less hazardous than its benchmark. For instance, if a mutual fund's beta is 0.95, the fund is somewhat less hazardous than its benchmark.
If the beta was 0.6 or 0.65, the fund would be less risky or volatile than its benchmark.
This is what relative risk refers to; it offers us an idea of how risky the fund is relative to its benchmark.
Therefore, if the beta of a mutual fund is 1, then the fund has the same level of risk as its benchmark. For instance, if the benchmark decreases by 1%, the fund should also decline by 1%. Hence, both the benchmark and the fund are anticipated to have comparable risk profiles.
If the beta of a fund is greater than 1, it indicates that the fund is riskier than its benchmark. A beta of 1.2, for example, indicates that the fund is 20% riskier than its benchmark. If the benchmark falls by one percent, the fund is anticipated to decline by 1.2%.
When looking at the Beta of a stock or an MF, it is critical to remember that the beta is a measure of relative risk; it shows us how dangerous the stock or MF is in comparison to its benchmark. Beta does not indicate the underlying risk of a stock or mutual fund.
To put this in context, consider the following: Ferrari is faster than BMW in this comparison, which is similar to the beta. We compare the speeds of car one and car two. But does this tell you anything about how fast the Ferrari is? Not at all.
Thus, while beta provides a view on the relative riskiness of an asset, it does not provide an absolute or inherent risk of the asset itself.
You must have formed an opinion of beta by now. Let me ask you this: do you think it's bad if a mutual fund has a high beta.
Well, the good, bad, ugly part of beta depends on another metric called the ‘Alpha ’.
Alpha
In the previous chapter, we briefly discussed alpha. Alpha is defined as the fund's excess return over and above the benchmark returns. That is correct, but we need to make a few minor adjustments to the equation to include our newly introduced friend, beta. To comprehend alpha, we must first comprehend the concept of 'risk-free' return. The risk-free return is the highest possible return without taking any risks. I mean market risk, credit risk, interest rate risk, and unsystematic risk when I say risk.
There are t wo return sources which fit in the above definition – (1) The return from the savings bank account (2) The fixed deposit return.
The treasury bills have an implicit sovereign, so it's deemed safe. The T-bill rates as of today are roughly about 8.3%.
Alpha is defined as the excess return of the mutual fund over the benchmark return, on a risk-adjusted basis.
Risk-adjusted basis means we need to –
- Calculate the difference between the mutual fund returns and the risk-free return
- Calculate the difference between the benchmark return and the risk-free return, multiply this by the beta
- Take the difference between 1 and 2
Mathematically,
Alpha = (MF Return – risk free return) – (Benchmark return – risk free return)*Beta
Let's put this in context with an example. Assume a certain fund gives you a return of 12%, its benchmark returns for the same duration is 10%. The beta of the fund is 0.75. What do you think of the alpha assuming the risk-free rate is 8?
Let’s apply the formula and check –
Alpha = (12%-8%)-(10%-8%)*0.75
= 2.5%
As you can see, the alpha is not just the difference between the fund and its benchmark, which if true, the alpha would have been –
12% – 10%
=2%
But rather, the alpha is 2.5%.
You may question where the additional 0.5% comes from.
Consider this: the fund has managed to earn a 12% return compared to the Index's 10% while remaining substantially less volatile (remember beta is just 0.75). As a result, we are rewarding the fund for its less volatile behavior. As a result, the alpha is 2.5% rather than 2%.
Consider the identical fund with the same returns, but with a beta of 1.3 instead of 0.75. What do you think the alpha is?
By now, you should guess that since the beta is high, the fund gets penalized for its erratic behavior. Therefore the alpha should be lower.
Let us see if the numbers agree to this thought.
Alpha = (12%-8%)-(10%-8%)*1.3
=1.4%
Even though the returns stay the same, thanks to beta, the alpha is much smaller when risk is taken into account.
In the end, alpha is the difference between the fund's return and the benchmark return. Alpha is risk-adjusted. The fund gets a bonus if the returns come from keeping a low-risk profile, and it gets a penalty if it is volatile.
You should know by now that volatility is an important part of figuring out how well a mutual fund is doing. Beta is a way to measure how volatile something is. It tells us how risky a fund is compared to its benchmark. Beta is a relative risk that doesn't tell you anything about the fund's own risk. The inherent risk of a fund is revealed by the ‘Standard Deviation’ of the fund.
Standard Deviation (SD)
The standard deviation of a stock or a mutual fund represents the riskiness of the stock or the mutual fund. It is a percentage, expressed as an annualized figure. The greater the standard deviation, the greater the asset's volatility. The greater the volatility, the greater the risk.
Loss = Investment * (1-SD)
Gains = Investment * (1+SD)
The larger the SD, the larger the possibility of loss or gains.
In general, the SD for mid- and small-cap funds is more than that of large-cap stocks.
Note that volatility and Standard Deviation should not cause you concern. Markets are inherently volatile, as are stocks and mutual funds. Volatility is inherent to markets. If you cannot stomach seeing your investment fluctuate between profits and losses, you may want to reconsider your decision to invest in shares.
Yet, if you choose to invest in stocks, you must learn to manage volatility.
There are two techniques to tame the beast known as "Volatility":
● Diversify smartly (and not over diversify)
● Give your investment time
Time is the ultimate remedy for volatility. Give time to your investments, and time will eliminate volatility.
Sharpe Ratio
Sharpe Ratio is one of the most recognized financial concepts. It was developed in 1966 by the American economist William F. Sharpe. In 1990, he was awarded the Nobel Prize for his contributions to the Capital asset pricing model.
Imagine there are two large-capitalization funds, A and B. Here is their performance in terms of returns —
Fund A – 14%
Fund B – 16%
Which of the funds is superior? Fund B has a higher return, hence it is without a doubt the superior fund.
Now consider the subsequent –
Rf is the return without risk. The standard deviation/volatility/risk of the two funds are also mentioned alongside their returns. Which of the two funds do you believe is superior?
Ignoring the risk, purely on a return basis, Fund B is better. Ignoring the return, purely on a risk basis, Fund A is better. But in reality, you cannot isolate risk and reward; you need to factor in both these and figure out which of these two are better.
The Sharpe Ratio helps us here. It bundles the concept of risk, reward, and the risk-free rate and gives us a perspective.
Sharpe ratio = [Fund Return – Risk-Free Return]/Standard Deviation of the fund
Let's apply the math for Fund A –
= [14% – 6%] / 28%
= 8%/28%
= 0.29
The value indicates that the fund delivers 0.29 units of return (above the risk-free rate) for each unit of risk taken. By definition, the larger the Sharpe ratio, the better it is, as we all desire greater rewards for each unit of risk undertaken.
Let’s see how this turns out for Fund B –
= [16% – 6%] / 34%
= 10% / 34%
= 0.29
So it turns out that both the funds are similar in terms of their risk and reward perspective. And there is no advantage of choosing Fund A over Fund B.
Now, instead of 34% standard deviation, assume Fund B’s standard Deviation is 18%.
[16% – 6%] / 18%
= 10% / 18%
= 0.56
In this case, Fund B is a better choice because Fund B generates more return for every unit of risk undertaken.
Do note, Sharpe ratio considers only price based risk. It does not consider credit or interest rate risk. Hence, there is no point looking at the Sharpe ratio for debt funds.
In the next chapter, we’ll discuss the Sortino’s ratio and the Capture ratios and conclude our discussion on Mutual Fund risk parameters and then shift focus on building Mutual Fund portfolios.
