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.

Why not,

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.

bharat shahi like the conclusion:'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.' i only like liquid funds or short term/ultra short term funds on debt side.

pattuPost authorThank you. I agree with you. So do I.

bharat shahi like the conclusion:'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.' i only like liquid funds or short term/ultra short term funds on debt side.

pattuPost authorThank you. I agree with you. So do I.

EswarIt's a very interesting analysis, I guess your training as a scientist is coming to fore here with looking at the same data differently and extracting as much information as possible. I learn something new every time I read your blog, keep up the good work.

pattuPost authorThank you very much.

EswarIt's a very interesting analysis, I guess your training as a scientist is coming to fore here with looking at the same data differently and extracting as much information as possible. I learn something new every time I read your blog, keep up the good work.

pattuPost authorThank you very much.

DeepHmm..enlightening as always...The most important part i think is that liquid funds and long term debt are returning almost same.Which means it is almost a no brainer to go for liquid funds as both credit risk and volatility risk are lowest.

pattuPost authorThanks, Deep. Precisely. Long-term debt funds are not suitable for buying and holding. Interest rate are cyclic. They do not move northward like markets do.

DeepHmm..enlightening as always...The most important part i think is that liquid funds and long term debt are returning almost same.Which means it is almost a no brainer to go for liquid funds as both credit risk and volatility risk are lowest.

pattuPost authorThanks, Deep. Precisely. Long-term debt funds are not suitable for buying and holding. Interest rate are cyclic. They do not move northward like markets do.

PushkarHi,

I had a question, why returns of liquid funds is around 5% in the years 2004,2005,2009 & 2010.

As per table provided for Kotak Liquid fund ?

Is it because of low interest rates at that time ? My concern is, even at that time, the FD rates were around 7-8% ( I am not sure), so why less returns for Liquid funds ?

Is it because earlier liquid funds has instruments with longer maturity duration ?

At present daily 0.02% is approx rise in Liquid funds. Is there any way if future returns of liquid funds are like these 5% ?

Thanks

pattuPost authorGood point! This is true of many liquid funds. Don't know the reasons but it is not because of longer maturity duration. It is the other way around. They only hold debt paper that matures within 90 days. They will remain volatile in the future too. That is why there is no guarantee that post-tax liquid fund return will beat post-tax FD!

PushkarOk, but does this rule about holding debt paper that matures within 90 days was applicable even in 2005 ? Because earlier they had a rule of 180 days. So asked.

Is there any way to identify when the returns from liquid fund will start deteriorating? Means as I said there is a daily 0.02% is approx rise in NAV, if the increase is less than that for prolonged period of say 1-2 months, can it be a alarm ?

Or does it depend on "current short term interest rate" and if banks reduce the int rates, the liquid funds would also be affected ?

Thanks.

pattuPost authorIt is 91 days now. See the dates here:

http://www.hdfcfund.com/Products/SchemeDetails.aspx?SchemeID=222adc9c-3c47-45ae-80b7-aafaa8ab6bd1

It is difficult to predict NAV movement based on interest rate movement. There can be sudden developments like July 2013.

See

http://capitalmind.in/2013/07/liquid-funds-navs-fall-for-the-first-time-in-5-years/

PushkarHi,

I had a question, why returns of liquid funds is around 5% in the years 2004,2005,2009 & 2010.

As per table provided for Kotak Liquid fund ?

Is it because of low interest rates at that time ? My concern is, even at that time, the FD rates were around 7-8% ( I am not sure), so why less returns for Liquid funds ?

Is it because earlier liquid funds has instruments with longer maturity duration ?

At present daily 0.02% is approx rise in Liquid funds. Is there any way if future returns of liquid funds are like these 5% ?

Thanks

pattuPost authorGood point! This is true of many liquid funds. Don't know the reasons but it is not because of longer maturity duration. It is the other way around. They only hold debt paper that matures within 90 days. They will remain volatile in the future too. That is why there is no guarantee that post-tax liquid fund return will beat post-tax FD!

PushkarOk, but does this rule about holding debt paper that matures within 90 days was applicable even in 2005 ? Because earlier they had a rule of 180 days. So asked.

Is there any way to identify when the returns from liquid fund will start deteriorating? Means as I said there is a daily 0.02% is approx rise in NAV, if the increase is less than that for prolonged period of say 1-2 months, can it be a alarm ?

Or does it depend on "current short term interest rate" and if banks reduce the int rates, the liquid funds would also be affected ?

Thanks.

pattuPost authorIt is 91 days now. See the dates here:

http://www.hdfcfund.com/Products/SchemeDetails.aspx?SchemeID=222adc9c-3c47-45ae-80b7-aafaa8ab6bd1

It is difficult to predict NAV movement based on interest rate movement. There can be sudden developments like July 2013.

See

http://capitalmind.in/2013/07/liquid-funds-navs-fall-for-the-first-time-in-5-years/