We choose a type of instrument almost solely based on the kind of returns that it can yield. Thus, our expectation is governed by past history. While there is nothing wrong with this, past returns can vary quite a bit, and depends on the period chosen for evaluation.
While it is a good idea to base expectations on past history, only must also understand and appreciate the uncertainty associated with the expectation. The uncertainty will depend on the type of instrument and the duration of intended investment.
Regular readers know that I am a fan of the standard deviation and would recall that it can be used to select mutual fund categories suitable for financial goals.
The standard deviation listed by mutual fund portals like Value Research, Money Control, Morning Star etc. are typically based on monthly/weekly returns. While they can be used to represent the expected volatility associated with an instrument, they are not an accurate representation of the volatility or the uncertainty associated with past returns and therefore with future returns.
1) consider past annual returns of an instrument,
2) calculate the arithmetic average (not CAGR which is the geometric average),
3) calculate the associated standard deviation of the annual return,
4) Assume the arithmetic average ~ the expected future return from the instrument, plus or minus the standard deviation.
An example might help:
Let us consider the annual returns of Kotak Liquid Fund (source Value Research online)
The arithmetic mean or average = 7.33%
The standard deviation is 1.91%
So if I wanted to invest in Kotak Liquid, I will expect a return of about 7% give or take 2% (1.91 is approximated to 2%)
That is I will expect a return from 7% -2 % = 5% to 7%+2% = 9%
Calculating standard deviation this way, gives me a better idea of the range over which returns have fluctuated in the past. Although past performance may not repeat in the future, I have a foot hold with respect to expectations.
According to VR online, the fund has a standard deviation of 0.26%. Since this is calculated with monthly/weekly returns, it does not help me much since I am interested in annual returns.
The value of 0.26% when compared with corresponding data of other debt fund categories gives me an idea of relative volatility.
The value of 1.91% calculated with annual returns gives me an idea of absolute volatility.
This is how the standard deviation calculated with monthly/weekly returns evolves with respect to the average maturity of all debt fund portfolios.
Notice that region inside the red rectangle (< 1% standard deviation and < 1 year maturity) is heavily populated. These are liquid funds, ultra-short term funds, short-term income and gilt funds.
If the standard deviation of annual returns is used instead (below), notice that most of the points are outside the red rectangle.
Thus, if we use the standard deviation of annual returns, we find that even liquid funds are quite volatile. That is their annual returns can vary by a significant amount.
Higher the average maturity, higher the standard deviation in both cases.
Amusingly the 10 year CAGR (geometric average) is 7.31%. Not very different from the arithmetic average.
The difference between the two averages is another measure of relative volatility. The difference will be zero for a fixed deposit. Higher the difference, higher the volatility.
When the difference between the arithmetic average and the CAGR is plotted versus the average maturity in years of all debt fund portfolios, this is how it looks like.
Notice that the difference between the arithmetic average and CAGR is negligibly small for average maturity periods less than 1 year. Beyond that duration, the difference rapidly increases. However, even for the longest maturity periods (long term gilt funds), the difference is less than 1%.
Therefore, the simpler arithmetic average of annual returns is a pretty good alternative for the CAGR and could be set as the average return one can expect from a debt mutual fund.
The same will not be true for equity funds due to their much high volatility. We will consider these in another post.
The relative volatility (difference between arithmetic mean and CAGR) shares an interesting relationship with the absolute volatility (standard deviation of the annual return).
Notice how smoothly the curve evolves for all debt mutual funds. The evolution is faster than a straight line. Thus, the difference between the arithmetic average of returns and CAGR becomes more prominent at higher standard deviations.
Finally, a look at the CAGR of all debt mutual funds 10 years or older. This would give us an idea while planning for goals.
That does not paint a pretty picture at all!. The long-term return of funds with high average maturity (eg. long-term gilt funds) is comparable to funds with low average maturity (eg. ultra-short funds, short-term funds or even liquid funds)!!
Thus, if one wishes to invest in funds with high average maturity, they should actively manage the fund. That is, they should shift gains (to equity, for example) when interest rates drop, or invest more when the interest rates rise. A ‘buy and hold’ strategy with such funds may not be beneficial.
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