Mutual Fund Risk Exploring Beta, Alpha, and Standard Deviation

Beta

Over the last few chapters, we discussed various attributes of a mutual fund. We will continue the same in this chapter and focus on key risk measures of a mutual fund. Risk measures include various attributes such as –

• Beta
• Alpha
• Standard Deviation
• Sharpe Ratio

We will start with the beta.

An important attribute of a mutual fund is the ‘beta’, which expresses the relative risk as a numerical value. This metric gives us an understanding of how risky the fund is compared to its benchmark figure. Beta can have any numerical value, both above and below zero.

From Value research I have gathered that Tata Multicap fund has a benchmark of S&P BSE 500 TRI.

The beta of the fund is 0.95, which gives us an indication of its relative risk. As previously mentioned, this measure offers insight into the potential volatility of the fund.

The Tata Multicap fund has a beta of 0.95, indicating it is somewhat less risky than its benchmark. This means that if the S&P Sensex 500 sees a 1% decline, the Tata Multicap fund can be expected to dip by 0.95%. Since this number is close to 1, the difference in risk remains relatively small.

A beta of 0.6 or 0.65 indicates that Tata Multicap fund is less risky and its volatility is lesser compared to the benchmark S&P Sensex 500. This is due to the fact that if S&P Sensex 500 experiences a 1% dip, we can assume that Tata Multicap Fund will fall by only 0.65%, instead of the expected 0.95%.

This gives us an insight into the relative risk of the fund, demonstrating how it stacks up against its benchmark.

In cases where the beta of a mutual fund is equal to 1, it means that its risk profile should be identical to that of its benchmark. This means that if the benchmark drops by 1%, then the fund can be expected to experience a similar decrease.

If the fund’s beta is greater than 1, it demonstrates that the fund is more hazardous in comparison to its benchmark. For instance, with a beta of 1.2, that implies the fund is 20% more perilous than its benchmark. If the benchmark decreases by 1%, then the fund will be expected to drop by 1.2%.

When looking at the Beta of a stock or mutual fund, it is key to note that it serves as a measure of relative risk- telling us how much more (or less) risky the security is compared to its benchmark. However, Beta does not reflect the inherent risk of an individual stock or MF.

To contextualise, comparing a Ferrari to a BMW is like looking at beta – it measures one car’s speed against the other’s, but doesn’t reflect how fast the Ferrari actually is.

Conversely, beta provides us with an assessment of the comparative risk of a certain asset, without indicating its definite or intrinsic hazard.

It’s clear that you now have formed your own opinion of beta. Here’s something to consider – is a mutual fund with a high beta necessarily bad?

Well, the good, bad, ugly part of beta depends on another metric called the ‘Alpha’.

– Alpha

In the preceding part, we briefly touched upon alpha. We defined it as the excess return of a fund compared to benchmark returns. However, this equation needs slight alterations and beta needs to be included as well. In order to comprehend alpha, it is imperative to be aware of the concept of ‘risk-free’ return. This is the most one can obtain without risking capital in terms of market risk, credit risk, interest rate risk and unsystematic risks.

The two options which can be considered for returns are savings bank account returns and fixed deposit returns.

Of course, we can argue that the banks too are not safe and comes with some degree of risk. Understandable, but let’s keep that argument aside for this discussion 😊

If you are particular about definitions, let us settle on treasury bills issued by the Indian government. It is known to be safe as it carries sovereign guarantee.

The T bill rates are currently estimated to be around 3.75%, and for our purposes, let’s use 4%.

Alpha is defined as the outperformance of a mutual fund with reference to its benchmark 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

Assuming a fund has a return of 10% and its benchmark returns 7% over the same period, with beta at 0.75, then the alpha with the risk-free rate at 4% can be calculated.

Let’s apply the for formula and check –

Alpha = (10%-4%)-(7%-4%)*0.75

= 6% – 2.25%

= 3.75%

You can observe that the alpha is not just determined by the contrast between the fund and its benchmark; if that were accurate, the alpha would have been –

10% – 7%

=3%

But rather, the alpha is 3.75%.

Now, many of you may not find this intuitive. You may question where the additional 0.75% comes from.

The fund has brought in a 10% return that surpasses the Index’s 7%, with notable stability (beta of 0.75). Consequently, rewards are being given to the fund for its steady performance – alpha is 3.75%, up from 3%.

Instead of a fund with a beta of 0.75, envision one with a 1.3 reading; what do you reckon its alpha is?

It is evident that a high beta leads to a penalty for erratic behaviour of the fund, thus resulting in a lower alpha.

Let us see if the numbers agree to this thought.

Alpha = (10%-4%)-(7%-4%)*1.3

= 6% – 3.9%

= 2.1%

Look at this: the returns stay the same, but due to beta, the alpha is greatly diminished when taking risk into account.

In conclusion, alpha is the extra return of the fund compared to benchmark returns. This is a risk-adjusted measure; funds that manage to produce returns with a low-risk profile are rewarded, while high volatility results in penalties.

By now, it should be clear that volatility is an integral factor in assessing mutual funds performance. Beta is a measurement of volatility; more precisely, it tells us how hazardous the fund is in comparison to its benchmark. Yet beta just provides a relative risk; the fund’s inherent risk still needs to be determined.

The inherent risk of a fund is revealed by the ‘Standard Deviation’ of the fund.

– Standard Deviation (SD)

I would recommend reading the whole chapter to get an understanding of standard deviation and volatility. It will aid you not only in mutual fund investments, but also stock investments.

I’m going to forgo further discussion of standard Deviation since it has already been addressed. In case you’re not keen on delving into a chapter to understand the concept, here’s a quick summary.

• The standard deviation of a stock or mutual fund illustrates the level of risk the security carries.
• Standard Deviation is a percentage, expressed as an annualised figure
• Higher the standard Deviation, higher is the volatility of the asset. Higher the volatility, higher is the risk.

For example, consider these two funds –

This snapshot was sourced from Value research and it concerns Axis Small-cap and Axis long term equity funds.

The SD of the small-cap fund stands at 23.95%, much higher than that of the long term equity fund which is 19.33%. This implies that the small-cap fund is significantly riskier when compared to the long term equity fund.

To set this in context, a Rs.10,000/- investment across funds can yield any outcome from profit to loss at the close of the year.

Loss = Investment * (1-SD)

Gains = Investment * (1+SD)

The larger the SD, the larger the possibility of loss or gains.

Speaking generally, mid and small-cap funds tend to have higher SDs than large-cap stocks.

It’s important to bear in mind that fluctuations in value or Standard Deviation are a part and parcel of investing in the markets. Whether it be stocks, mutual funds, or something else, volatility is simply an inherent feature of these investments. If being subject to fluctuating gains and losses doesn’t suit you, it may be wise to evaluate whether or not investing in equities is suitable for you.

If you invest in equities, you must learn to handle volatility. There are two strategies for dealing with this unpredictable monster –

• Diversify smartly (and not over diversify)
• Give your investment time

I’m of the opinion that time is the best remedy to volatility. If you give your investments some time, the volatility will be taken care of. Throughout this module, I have not only mentioned but also accentuated the importance of giving your Mutual Funds time, and this is exactly why I put so much emphasis on it.

Anyway, while at it, check the Alpha and Beta of both these funds. Few observations –

• Both the funds have a beta of below 1, which demonstrates that these funds are less risky than their benchmark. To determine how volatile each one is we can analyse their standard deviations.
• Alpha is a beneficial figure for both the funds. The Alpha of Axis small-cap fund stands out in particular, likely attributed to the low beta ratio and the current low risk-free returns in the economy.

Now that the risk parameters have become more clear, let’s shift our attention to another measure known as the ‘Sharpe Ratio’.

 – Sharpe Ratio

The Sharpe Ratio is one of the most esteemed calculations in Finance, having been created by Willam F Sharpe in 1966. His work on the Capital Asset Pricing Model eventually earned him a Nobel Prize in 1990.

Assume, there are two large-cap funds -Fund A and Fund B. Here is how they have performed in terms of returns –

Fund A – 14%

Fund B – 16%

Which of the two funds are better? Well, Fund B has a higher return, so without a doubt, Fund B is a better fund.

Now, consider the following –

I’ve indicated the return of the fund and its level of volatility as measured by standard deviation. Taking these factors into consideration, which do you believe is the preferable selection?

It can be tricky to determine which of the two funds are preferable when taking into account their risk and return.

Without regard to reward, Fund A would be the safer bet, but when factoring in both risk and return, it becomes clear that Fund B is the more attractive option. Ultimately, it’s important to take into account both of these variables when determining which investment route to take.

The Sharpe Ratio assists us in this area by combining the ideas of risk, remuneration and the risk-free rate, which allows us to gain a new point of view.

Sharpe ratio = [Fund Return – Risk-Free Return]/Standard Deviation of the fund

Lets apply the math for Fund A –

= [14% – 6%] / 28%

= 8%/28%

= 0.29

The number tells us that the fund generates 0.29 units of return beyond the risk-free rate for every unit of measured volatility. This means that a higher Sharpe ratio is more desirable, as investors prefer to receive more reward for their investment risk.

Lets see how this turns out for Fund B –

= [16% – 6% ] / 34%

= 10% / 34%

= 0.29

It appears that Fund A and Fund B are similar in the context of risk and reward. Thus there is no real distinction when considering which one to choose.

Now, instead of 34% standard deviation, assume Fund B’s standard Deviation is 18%.

[16% – 6% ] / 18%

= 10% / 18%

= 0.56

Fund B is preferable due to its higher returns for every level of risk embraced.

Note that the Sharpe ratio considers only price-based risk and not credit or interest rate risks; thus, it is of little use when examining debt funds.

In the following section, I’ll cover Sortino’s ratio and Capture ratios in relation to Mutual Fund risk parameters. After which, I will move forward by constructing Mutual Fund portfolios.