Do you understand the risk associated with your mutual fund’s returns?

Given the destruction of value that we’ve seen over the past 18 months on the stock market, most investment portfolios have taken a beating. Thankfully, the past few months have seen a strong rally in the stock market but over a 3, 5 and 10 year period the Standard & Poor’s 500 index (an index of 500 widely traded large-cap stocks) is still in negative territory. There was a period during late 2007 and early 2008 when investors could purchase just about any mutual fund and see its value rise rapidly as the bull market charged on. Unfortunately in many cases these investors neglected to understand the volatility associated with these fund’s returns…. as the saying goes: easy come, easy go.

While this article is intended to help understand the risk adjusted returns of a mutual fund, I thought it would be interesting to contextualize this by focusing on those funds that have managed to defy the odds and perform strongly when so many other funds have struggled. I’ll then take a closer look at these funds to ascertain the level of risk associated with their returns.

Which funds have performed well over the past 3 years?

When ranking over 17 700 funds on their 3 year annualized return, the top 3 performers (according to Jemstep) have been as follows: In first place the Dreyfus Greater China Fund (DPCRX) with an average annual return of 19.78%*, followed by another Dreyfus fund, the Dreyfus Greater China A Fund (DPCAX) with 19.46% and in third place we have the Aim China I Fund (IACFX) with 18.68%. China it would seem has been the place to invest. All these funds have managed to return over 18% which is phenomenal when you consider that an investment in a US index tracking fund such as the Vanguard 500 Index Investor (VFINX) has delivered a very poor return of -8.27% over the same period. While percentages can sometimes be misleading, an investment of $ 10 000 in the Dreyfus Greater China Fund (DPCRX) made 3 years ago would currently be worth approximately $ 17 185 while an investment in the Vanguard 500 Index Investor (VFINX) would only be worth approximately $ 7 719. The numbers speak for themselves.

Hindsight is an exact science and on a pure return basis the Dreyfus Greater China Fund (DPCRX) would clearly have been the best fund to invest in 3 years ago, but would it still have been the best investment to make when we add the fund’s risk/volatility into the equation? In other words, when focusing on the risk adjusted return would the Dreyfus Greater China Fund (DPCRX) still have been the best fund to purchase 3 years ago? In order to answer this question we need a basic understanding of a fund’s risk.

Determining a fund’s level of risk

When you go to a roulette table and you want to bet on which color will come up, red or black, you can work out exactly what your odds are of winning. There are 37 potential outcomes (0 to 37) of which 18 are red, 18 are black and 1 is green. Once you know this, it is easy to calculate that you have less than a 50% chance of winning 18/37 (48.65% to be exact) and as your payoff is only 100%, in the long run the odds are stacked against you and you are destined to lose. Thankfully investing doesn’t have to be as risky as playing roulette, and – just like in roulette – there are statistical measures in investing that can assist you in determining which funds carry more risk (volatility) then others.

A simple measure of risk

While there are a number of statistics that measure the risk associated with a fund, in this example I will be focusing on standard deviation as a well known measure for this purpose. Although the name may sound complex, this measurement is a simple number that represents the historical volatility of a fund’s returns. Quite simply, the higher the number, the higher the volatility of a fund’s returns and therefore the higher the risk associated with the fund.

How does it work?

If a fund has a three year average annual return of 10% and a three year standard deviation of 25%, then two thirds of the time the fund’s annual return can be expected to fall between-15% and 35%. How is this calculated? Take the fund’s average return, 10% and add and subtract the standard deviation to find the range of expected returns. For example 10% – 25% = -15% and 10% + 25% = 35%. Therefore we have an expected range of -15% to 35%. In summary, standard deviation indicates the range a mutual fund’s return can be expected to fall two thirds of the time. Remember the higher the number, the larger the expected range, so the more volatile a fund’s returns are expected to be.

In the example above, while some investors have a higher risk profile and are willing to invest in very volatile funds in order to maximize their returns, more conservative investors would suffer endless sleepless nights if they were invested in a fund where their potential returns could range between -15% and 35%.

Bringing it all together

From the table above it is clear that:

• Fund B has performed better then Fund A over the past 3 years: past performance 13% > 10%
• Fund A has been less volatile/risky then Fund B: standard deviation 7 < 8.5

But which fund has performed better on a risk adjusted performance? To answer this we need to do a very simple calculation to work out which fund generated more return for each unit of risk.

Return per Unit of Risk (RUR):

Once we’ve done this calculation it is clear that Fund B offers the best risk adjusted performance.

It’s important to note that if the annualized return is greater than the standard deviation, the return per unit of risk ratio will be greater than 1. A ratio above 1 indicates that you are being adequately rewarded for the risk (as measured by standard deviation) associated with the fund, conversely a ratio of less than 1 may indicate that the fund in not producing a high enough return given the risk or volatility of its return.

Now, let’s take another look at the three top performing funds over the past three years. We asked the question whether these funds would remain the best performers after we added risk into the equation. Let’s have a look at the results.

The most obvious area of concern in the table above is that the highest return per unit of risk ratio is only 0.51. Therefore the numbers suggest that although these funds were the best performers over the past 3 years, their returns were extremely volatile. As the graph below clearly illustrates, being invested in the Dreyfus Greater China I (DPCRX) over the past 3 years has been a wild ride and certainly not one for the faint hearted. The fund has touched highs of $ 57.53 and lows of $ 16.27. In fact, if we had performed this exercise in late 2008 or early 2009, the fund’s three year performance would have been deep in negative territory.

3 year price history for the Dreyfus Greater China Fund I (DPCRX)

Top performers – risk adjusted returns

So which funds have produced the best risk adjusted returns over the past 3 years? In order to calculate this you can simply use Jemstep’s Expert mode setting and ensure that you slide the 3 year standard deviation and 3 year total returns sliders all the way to the right. This efficiently ranks which funds have produced the highest return per unit of risk or, in other words, which funds have produced the highest returns with the lowest volatility. The results are as follows:

The above ranking suggests that on a risk adjusted basis the best performing funds over the past three years have been bond funds. Note that all of the above funds have a return per unit of risk ratio well in excess of 1 – this compares very favorably when compared to the high flying top performers over 3 years. In fact, Jemstep shows that once we add volatility/risk into our ranking, the Dreyfus Greater China Fund I (DPCRX) falls from first place to number 8 441 out of 17 700 funds. This is a drastic fall and a clear indication of how volatile/risky the returns have been with this fund.

So before you rush out to buy a “top performing fund” make sure that you are aware of the risks associated with the fund.