Measuring Mutual Fund Risk with Alpha, Beta, R-Squared, Standard Deviation and Sharpe Ratio

Measuring Mutual Fund Risk with Alpha, Beta, R-Squared & Sharpe Ratio

Mutual Fund risk is measured by using statistical measurements that are historical predictors of investment risk and volatility. These risk statistics form the basis for many decisions in investing and finance. The most prominent measures include alpha, beta, R-squared, standard deviation and sharpe ratio. In this article, we shall examine each of these risk measures in greater details

The five principal mutual fund risk measures are –

  1. Alpha
  2. Beta
  3. R-squared
  4. Standard deviation and,
  5. Sharpe ratio

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Alpha

Alpha (also called the “holy grail of investing”) measures the performance of an investment portfolio against its benchmark index.

The alpha is the difference between the returns of your portfolio and the returns of the benchmark – which means the alpha can be positive or negative. A positive alpha of one means the portfolio has outperformed the benchmark by 1 percent. Likewise, a negative alpha indicates the underperformance of an investment.

What is alpha is zero?

An alpha of zero would indicate that your investment portfolio or mutual fund is moving perfectly with the benchmark index. In other words, the portfolio manager has not added or lost any value when compared to the broad market.

Got it. Is alpha important?

Oh yes!


Importance of Alpha

Alpha is quite a significant number when evaluating mutual fund risk. E.g. Franklin India Bluechip Fund uses NIFTY 100 TRI as its benchmark. Over a 5-year period, Franklin India Bluechip Fund has delivered a CAGR of 13.92% while the benchmark has delivered 13.54%, which translates to an alpha of 0.38.

However over a 3-year period, Franklin India Bluechip Fund and the NIFTY 100 TRI have delivered 12.76% and 17.41% respectively. So, on a 3-year evaluation, the alpha for the Franklin India Bluechip fund is -4.65.

Fund managers and hedge fund managers love to talk about their alpha indicating that they are good enough to outperform the market and deliver above-average returns to their clients.

How does all this help me?

As an investor, it’s important for you to check what benchmark are the fund managers using. Case in point is the Aditya Birla Sun Life Frontline Equity Fund, also a large cap fund, which uses NIFTY 50 TRI as its benchmark. As a result, the alpha for this large cap fund make a very different reading.

3 year alpha = -3.11 (Fund : 14.59%, Benchmark : 17.70%)

5 year alpha = 2.26 (Fund : 15.65%, Benchmark : 13.39%)

While alpha is highly desirable in one’s portfolio, many benchmarks manage to beat actively managed funds like Franklin India Bluechip Fund (AUM of ₹7,500 crores) and Aditya Birla Sun Life Frontline Equity Fund (AUM of ₹20,000 crores).

Evidence shows that in the United States, 83% of active funds have been unable to deliver a positive alpha over a 10 year period. This number goes further up when you add other expenses like taxes and fees. In the Indian context too, we have seen evidence of that with the 3 year performance of both mutual funds. As a consequence, more and more investors are switching to low-cost, passively managed Index funds with the rationale being, “if you can’t beat them, join them”.

The difference between active and passive mutual funds is falling with the alpha being as low as 0.5% (down from 6.5%). Source: Is it time for you to shift from large-cap to passive mutual funds?

Beta

Beta measures the relative volatility of a portfolio or mutual fund against its benchmark index. This volatility or swing gives you the systematic risk of the security or portfolio when we compare it to the market as a whole. A beta greater than one indicates higher-than-benchmark volatility and vice-versa.

At the time of posting this blog, the Franklin India Bluechip Fund and Aditya Birla Sun Life Frontline Equity Fund both operated at a beta of 0.94. The ICICI Prudential Value Discovery Fund which has an AUM of ₹15,000 crores has a beta of 0.67 . And the HDFC Top 100 Fund, also having an AUM of ₹15,000 crores has a beta to 1.07.

OK. So should I go for high or low beta?


A popular notion among financial advisors is that a risk-averse investor will prefer a beta of lower than one. On the other hand, an aggressive investor who is ready to compensate with higher mutual fund risk for higher returns would prefer a higher beta.

That might be true to the extent of volatility expectations but unfortunately, it renders a false notion amongst consumers that lower volatility means lower mutual fund risk – which is not exactly related.

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Lower volatility may not mean lower risk

It’s a lot like you comparing two batsman who in their last 10 games of cricket have scored the following runs –

Batsman A – 30, 45, 32, 48, 29, 35, 31, 38, 27, 35

Batsman B – 71, 5, 29, 101, 12, 0, 4, 0, 119, 9

Both measures (alpha and beta) need to be used in calculation, comparison and prediction of investment returns.

Investors should clearly understand the different between what alpha and beta aims to explain.

To reiterate, alpha is the risk-adjusted measure of how a security or portfolio performs when compared to the overall market return. The loss or profit achieved relative to the benchmark represents the alpha. Beta measures the relative volatility of a security or portfolio when compared to the average volatility of the market.

I contend that a higher beta can be a boon in disguise because it works both ways. A stock with a beta of 2 (relative to the index) goes up or down twice as much as the index in a given period of time. The way I look at it is that if I can find an under-valued stock in a lagging market with a high beta, there is an excellent probability of making a killing when the broader markets start looking up.

R-squared

R-squared measures the explained movement of a fund or security in relation to a benchmark.

Unlike what some beginners believe, it is not a measure of portfolio performance. Even a great portfolio can have a very low R-squared. It is simply a measure of the correlation of the portfolio’s returns to the benchmark’s returns. In other words, if you want a portfolio that moves like the benchmark, go for a portfolio with high R-squared.

R-squared ranges from 1 to 100. An R-squared of 100 indicates that your portfolio exactly mimics the benchmark index’s movements.

What’s an example of a 100 R-squared?

An example of this are index funds. Such funds invest only in indices like the S&P 500 (United States) or Nifty 50 (India) stocks. Index funds will have an R-squared very close to 100.

On the other end, a low R-squared means much lower amount of a portfolio’s movements can be explained by movements in its benchmark index. An R-squared measure of 30 means that only 30% of the portfolio’s movements are aligned to the benchmark index movements.

Got it?


R-Squared in Mutual Funds

Let’s see how that works in a mutual fund environment. Here are three funds with different R-squared measures –

Although the benchmark on all three funds are different, I don’t see too much of difference here to nullify the comparison and the core objective of this exercise.

The R-squared on these three funds indicate that index funds always tend towards an R-squared of 100 as shown in the data related to HDFC Nifty 50 Index Fund.

In the case of the ICICI Prudential Bluechip Fund, we see a very high R-squared number. This is because a large cap fund also tracks closely to the movements of its benchmark i.e. Nifty 50 or Sensex or Nifty 100. These indices covers India’s top 100 listed companies.

The TATA Equity PE fund shows a low-to-mid correlation with the benchmark returns. This is because this fund is a value fund which does not mimic the benchmark i.e. S&P BSE Sensex TRI. The fund manager exercises his/her stock picking skills to pick companies to invest in based on the analysis put forward by his team. We can see this in the below chart where the fund has fewer proportion of it’s investments in financial stocks as compared to the benchmark.

The TATA Equity PE Fund stock selection are at variance to its benchmark’s industry allocation

Rules for R-Squared measures

  • 70-100% = good correlation between the portfolio’s returns and the benchmark’s returns
  • 40-70% = average correlation between the portfolio’s returns and the benchmark’s returns
  • 1-40% = low correlation between the portfolio’s returns and the benchmark’s returns

Thus, I can use R-squared numbers in conjunction with other statistical measures to help weed out redundant holdings. This helps me build a well-diversified portfolio.

Come to this of it, I have just explained in greater detail this strategy which helped me increase my returns by 9% with no increase of mutual fund risk in my portfolio. This is done by replacing a good portion of actively managed funds with index funds when both these type of funds displayed similar risk behaviour. The 9% improvement comes on account of lower expenses in index funds which gives me a better alpha.

Loving it. What else?

R-squared investing is also an excellent diversification measure and is a part of my stock diversification strategy. A good diversification need not be only industry specific but statistics can also help.


Standard Deviation

Standard deviation quantifies any variation from the average return (mean) of a data set. In finance, standard deviation uses the average return from a stock or portfolio to measure the investment’s volatility.

Standard deviation differs from beta to the extent that beta compares volatility with a benchmark index while standard deviation measures volatility from the historical data of the same instrument.

Standard deviation is a popular measure of mutual fund risk.

High standard deviations are indicative of volatility while low standard deviations are associated with stable assets.

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Lets examine two mutual funds.

Fund A and Fund B started asset management with an NAV of ₹100. The month-end NAV of the last 10 month until present day is available in the table below.

While Mutual fund A and Mutual fund B start and end with the same NAV, the standard deviation of both funds are quite very different

We see that Fund A displays a standard deviation of 2.86. And Fund B has a standard deviation of 8.31.

The significance of these numbers can be understood when plotting these in a normal distribution curve. The approximate data distribution around the mean with increasing standard deviation are :

  • 68% .. for +/- one standard deviation
  • 95% .. for +/- two standard deviations
  • 99.7% .. for +/- three standard deviations

If you’d like to know how standard deviation is calculated the old-fashioned way (before MS Excel changed our way of life), check out this post on Step-by-Step Calculation of Standard Deviation by the Khan Academy

But why do you want to do that!

Just go to MS Excel and use the STDEV function.

Thus, for Fund A, in 99.7% of the occasions, the range of values will be within three standard deviations from the mean. In other words, the range for Fund A based on the last 10 months of historical data will be 91.42 to 108.58.

Here’s how we got there –

  • Mean = 100
  • One standard deviation = 2.86
  • Three standard deviations = 8.58
  • Lower Range = 100 – 8.58 = 91.42
  • Upper Range = 100 + 8.58 = 108.58

Exercise for you

Try a similar approach with Fund B where the mean is 100 and one standard deviation is 8.31. Write your answer in the comments section of this blog post.

The above exercise shows that Fund B has a higher standard deviation as compared to Fund A. Since both funds have given the same return – Fund B carries a higher risk when compared to Fund A.

This is where it gets a little tricky and I have maintained all through the post that “stable” should not be construed as safe or better assets.

But it’s not that simple.


Statistics can confuse you

Let’s understand this with two more mutual funds – Fund C and Fund D.

Fund C has been increasing it’s NAV by ₹1 for the last 10 months. And Fund D’s NAV has been dropping by ₹1 for the last 10 months.

As a result –

  • Fund C has a mean of 105 with a standard deviation of +/- 3.16
  • Fund D has a mean of 95 with a standard deviation of +/- 3.16
While the standard deviation is the same for Mutual fund C and Mutual fund D, we observe that the performance of the funds have been very different. Proves that we can’t look at standard deviation in isolation and needs to be seen with other measures

Fund C and Fund D have the same standard deviation! But it will require some convincing to get me to put both funds in the same risk standing.

The point here is that standard deviation is a guiding light but not a stoic statistic on which decisions can be taken. It has to be looking in association with other mutual fund risk measures like alpha, beta, sharpe ratio and R-squared.

Sharpe Ratio

The Sharpe Ratio measures the expected excess return of an investment in relation to its return volatility.

In other words, the Sharpe ratio aims to determine how much additional return an investor can receive with the additional volatility on account of holding riskier assets.

A Sharpe ratio of 1 or more is considered to be a better risk-to-reward proposition for the investor. Also, when comparing two assets versus a common benchmark, the one with a higher Sharpe ratio provides better return for the same risk.

Here are the Sharpe ratios of some mutual funds –

Sharpe ratios are often used to rank the performance of mutual funds.

Is Sharpe ratio a good measure?

For it’s popularity, a major complaint about the Sharpe ratio is that it relies on the notions that risk equals volatility. And that volatility is bad.

I have said it before and will repeat it – volatility is not the enemy but a huge opportunity which allows smart investors to achieve excellent alpha.

The Sharpe ratio treats all volatility equal and thus penalizes approaches which have upside volatility leading to big positive gains in performance.

The Sharpe ratio should be used as a comparative tool and investors should not look at it in isolation.

In case of mutual funds, you can compare the Sharpe ratio of a fund with its benchmark index to get a better understanding of excess return and mutual fund risk.

If the only information available is that the Sharpe ratio of a fund is 1.2, no meaningful inference can be drawn as nothing is known about the peer group performance.

Another flag you need to watch out for relates to funds which have low returns but since they have a relatively mild standard deviation, they can show up pretty high on the Sharpe ratio listings.


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