Evaluating Volatility in Returns

Use this rolling standard deviation calculator to evaluate  the volatility in returns of  a mutual fund.   This is an idea that struck me during the Chennai investor meet in response to a question.

The sheet calculates the rolling return and rolling standard deviation for a specified interval. For equity funds, the rolling standard deviation of the fund can be compared with its benchmark.

One can also compare the rolling return of the fund with its rolling standard deviation.

The standard deviation is a measure of how much returns can deviate from the average return. In fact, the standard deviation is the average deviation.

Higher the standard deviation, higher the volatility in return.

The standard deviation is calculated from daily returns and then annualized by multiplying it with the square root of the number of trading days (250-252) in a year.

I have mentioned about the importance of the standard deviation in the following posts.  If you are not familiar with the term, please read these posts and then use this sheet:

Here are some screenshots.

7-year rolling return of equity fund return and standard deviation

rolling-std-3

Although the std-dev variation looks dramatic, compared to the variation in returns it is quite small. However, the standard deviation is a steady ~ 22-23% and always higher  than the return.

This means the investing in HDFC equity for 7 years is fraught with risk. The volatility in returns can result in a risk in this case since the duration is low.  Note that 7 year returns have been plotted from April 2006 only. Had it been since inception, the fluctuation in return would have been much more.

That said, the fund has a lower standard deviation that its benchmark.  Thus, the fee paid to the fund manager is justified.

rolling-std-4

This is the corresponding rolling return.

rolling-std-2

1-year rolling return of liquid fund return and standard deviation

rolling-std-5

The standard deviation of a liquid fund is 100 times lower than an equity fund!  However, due to debt market movement the spread in the returns in not proportionally lower and there is still significant volatility in returns.

That is, the actual return for a 1- year investment in a liquid fund will depend on when you started investing.  However,  it is safe to say that volatility will always be low.

For an equity fund, again the return will depend on when you start on investing. It is safe to say that, unless the duration is 15+ years, the standard deviation will be comparable to returns. That volatility will always be high.

The sharp vertical changes are due to discontinuity in dates and can be ignored. I do not know a way around this as of now.

Download the Rolling Returns + Rolling Standard Deviation Calculator

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4 thoughts on “Evaluating Volatility in Returns

  1. Krishnan

    Great post.

    Average Rolling returns and SD for various time periods is what I would characterize as profile of the investment.

    Years. 1. 2. 3. 4. 5
    Avg RR. 17. 16. 16.5. 16. 17
    Deviation. 30. 20. 14. 10. 9

    These graphs and profiles are nice to see, but where are we applying these.?

    When we move to goal based investments or any future projections we are asked enter a "expected rate of return". I cringe every time I enter 12% for equities and 8/9% for debts. We have all this rolling returns data already with us (based on past history) but these are not applied. Like a layman we enter some crude numbers and the calculator does not account for any uncertainty (SD) and spits out another cruder estimation.

    I raised this earlier and I know you weren't convinced. None of this is new to you, but let me try again. As we predict into the future there is degree of uncertainty involved. This is taken into to account by we software guys (in project estimation) and meterogists (and also in finance) and it is called the cone of uncertainity. Cone shape indicating that as we predict further into the future the uncertainty increases. The lower part of the cone indicates the worst case scenario and the upper part the best. I am suspicious of any prediction which doesn't show me a uncertainty band. There is a retirement planner from Microsoft which takes an uncertainty factor and generates a cone depicting worst/best case scenarios (the uncertainty in prediction)

    http://office.microsoft.com/en-us/templates/retirement-financial-planner-TC104022385.aspx

    Now instead of uncertainty range for each parameter (rate, inflation etc), I suggest that we make use of the investment's long term profile and use Avg (rolling returns) and corresponding SD (for each time period) in any calculator that is used for future prediction. In which case, you would end up with a band instead of just a line. A band is extremely useful for understanding what can go wrong.

    Interestingly, as we predict further into the future the avg rolling returns for a longer period stabilizes with a lower SD. So if done right, we may not end up with a cone but more a pipe or even a reverse cone. This is the only field I am aware of where we can predict long term future with more certainty compared to near term (and hence we safely recommend equities for longer term)

    My apologies for the long comment and bringing up this again. Just wanted to convey some ideas; don't really expect you to build calculator based on every fancy idea somebody comes up with.

    I am a hands-on Software Engineer by profession (managing our company's premier product in the financial domain) and know how hard it is to convert fancy ideas into usable software. Really appreciate your calculators.

    Reply
    1. pattu

      Thank you. In a volatile instrument, predicting does not help you much. I have made Monte Carlo simulators which can give this band. However, my view is to look at historical volatility and use the lower end of this number. Equity for 15Y returns about 15% +/- (4-5%). So I will not expect more than 10% no matter how long the goal is. The advantage is, I am calmer, invest more, churning is lower because expectations are lower.

      Reply
  2. Krishnan

    Great post.

    Average Rolling returns and SD for various time periods is what I would characterize as profile of the investment.

    Years. 1. 2. 3. 4. 5
    Avg RR. 17. 16. 16.5. 16. 17
    Deviation. 30. 20. 14. 10. 9

    These graphs and profiles are nice to see, but where are we applying these.?

    When we move to goal based investments or any future projections we are asked enter a "expected rate of return". I cringe every time I enter 12% for equities and 8/9% for debts. We have all this rolling returns data already with us (based on past history) but these are not applied. Like a layman we enter some crude numbers and the calculator does not account for any uncertainty (SD) and spits out another cruder estimation.

    I raised this earlier and I know you weren't convinced. None of this is new to you, but let me try again. As we predict into the future there is degree of uncertainty involved. This is taken into to account by we software guys (in project estimation) and meterogists (and also in finance) and it is called the cone of uncertainity. Cone shape indicating that as we predict further into the future the uncertainty increases. The lower part of the cone indicates the worst case scenario and the upper part the best. I am suspicious of any prediction which doesn't show me a uncertainty band. There is a retirement planner from Microsoft which takes an uncertainty factor and generates a cone depicting worst/best case scenarios (the uncertainty in prediction)

    http://office.microsoft.com/en-us/templates/retirement-financial-planner-TC104022385.aspx

    Now instead of uncertainty range for each parameter (rate, inflation etc), I suggest that we make use of the investment's long term profile and use Avg (rolling returns) and corresponding SD (for each time period) in any calculator that is used for future prediction. In which case, you would end up with a band instead of just a line. A band is extremely useful for understanding what can go wrong.

    Interestingly, as we predict further into the future the avg rolling returns for a longer period stabilizes with a lower SD. So if done right, we may not end up with a cone but more a pipe or even a reverse cone. This is the only field I am aware of where we can predict long term future with more certainty compared to near term (and hence we safely recommend equities for longer term)

    My apologies for the long comment and bringing up this again. Just wanted to convey some ideas; don't really expect you to build calculator based on every fancy idea somebody comes up with.

    I am a hands-on Software Engineer by profession (managing our company's premier product in the financial domain) and know how hard it is to convert fancy ideas into usable software. Really appreciate your calculators.

    Reply
    1. pattu

      Thank you. In a volatile instrument, predicting does not help you much. I have made Monte Carlo simulators which can give this band. However, my view is to look at historical volatility and use the lower end of this number. Equity for 15Y returns about 15% +/- (4-5%). So I will not expect more than 10% no matter how long the goal is. The advantage is, I am calmer, invest more, churning is lower because expectations are lower.

      Reply

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