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Unit Trusts – Pertinent Points To Consider When Investing In Funds (Part 2)
Education | 31 May 2010
By: jason.liew
Articles (66) Profile

After understanding your risk profile, the costs incurred in investing in the funds, as well as, how the fund managers manage the funds, the next important point to consider is the risk – reward profile of the funds.

Risk vs returns

First, the risk aspect

I will first discuss the first aspect i.e. the risk component. Studies have shown that past risk is quite a good indicator of future returns. I will discuss on the two common risk measures, viz. standard deviation and beta. In addition, the validity of beta has to be considered with respect to its R-squared which I will also explain in the paragraphs below.

Standard deviation

Investors are likely to be familiar with this measure. It is typically shown in fund factsheets and part of Statistics 101. Standard deviation measures how much the fund performance varies from the mean, or average. Naturally, the more dispersion of the fund performance from its mean, the more risky is the fund. I have tabulated some examples in Table 1 to familiar ourselves with standard deviation.

Examples to illustrate standard deviation
Table 1: Examples to illustrate standard deviation

For Scenarios 1 and 3, the fund registers an annual percentage return of +5% and -5% respectively. As there is no change in the yearly returns in each of the years, the standard deviation is zero for both scenarios. For Scenario 2, the standard deviation should be more than zero as the yearly returns change in each of the years.

In other words, standard deviation measures the range of returns the fund is likely to generate over a period of time. According to statistics, assuming a normal distribution, future yearly returns of the funds will likely fall within one standard deviation of its mean return 68% of the time and two standard deviations 95% of the time. This means that, for a fund with a mean return of 10% per annum and a standard deviation of 6%, there is a 68% chance that the fund is likely to register 4% – 16% returns (one standard deviation) and 95% chance for the fund to generate between -2% and 22% (two standard deviations) for the next year.


Beta measures the relative volatility vis-à-vis that of a benchmark. I.e. the higher the fund’s volatility, the higher the beta. Table 2 explains the significance of the various levels of beta.

Beta explained
Table 2: Beta explained

For beta to be of significance, it is paramount that the benchmark which the fund is being compared to is an appropriate benchmark. For example, given an Asia Pacific ex Japan fund, whose benchmark is S&P 500 Index, the beta on the fund sheet may not be as significant as another Asia Pacific ex Japan fund, which uses the MSCI Asia Pacific ex Japan Index for comparison. In order to gauge the “appropriateness” of the benchmark, we can examine another statistic called the R-squared.

R – squared

According to Investopedia, R-squared is a statistical measure that represents the percentage of a fund or security’s movements that can be explained by movements in a benchmark index. R squared range from 0 to 100. Given an R-squared of 100, it simply means that all of the fund’s return can be explained by the movements in the index. An R-squared of 0 would mean that none of the fund’s return is explained by the movements in the index. Therefore, the higher the R-squared, the higher the validity of the beta. As a general rule of thumb, we would disregard the beta if the R-squared is less than 75.

Next, the return aspect (adjusted for risk)

We typically analyse the following risk adjusted returns ratios to determine the attractiveness of the fund.


Alpha is the “value add” by the fund manager. It is calculated in the following way:

Alpha = Fund’s return – risk free rate – expected return based on beta

Illustration of calculation of alpha
Table 3: Illustration of calculation of alpha

Based on Table 3 above, the fund manager has a value add of 7%. There are some noteworthy points over the usage of alpha. Firstly, as the calculation of alpha is derived from the expected return based on beta, any drawbacks that affect beta would naturally affect alpha. Secondly, it is important that alpha does not differentiate between excellent fund management skill and good luck. However, if the fund managers continue to deliver consistent positive alpha over a period of decades, it is highly likely that the fund managers are skilled in fund management.

Sharpe ratio

Simply put, sharpe ratio measures the performance of the fund, adjusted for risk. In other words, sharpe ratio indicates whether a fund’s performance is attributed to astute stock picks or as a corollary of assumption of excess risks. This is based on the premise that portfolios which generate strong performance can only be considered as good investments if this performance does not come with undue excessive risk.

Sharpe ratio is calculated via this formula below:

Sharpe ratio = (Fund return – risk free rate) / fund’s standard deviation

Illustration of calculation of sharpe ratio
Table 4: Illustration of calculation of sharpe ratio

Similarly, the sharpe ratio of 2.2 will be more informative if we compare this either against a benchmark, or its peers. Generally, the higher the Sharpe ratio, the more attractive the fund is.

There are some advantages of sharpe ratio over alpha. Firstly, sharpe ratios are meaningful all the time, vis-à-vis the beta dependent alpha (alpha may not be meaningful if the beta is not meaningful – as measured by R-squared). Secondly, as sharpe ratio is not dependent on the choice of benchmark used, we can compare sharpe ratio of equity funds vs bond funds and determine which fund is more attractive.


Besides understanding your risk profile, the costs incurred in investing in the funds, how the fund managers manage the funds, investors should also pay heed to the risk reward profile of the fund. These are some of the pertinent factors to consider when investors are doing their research on the funds.

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