Understanding Volatility and Sharpe Ratio in Unit Trust Investing

Familiar with the following two jargon in unit trust investing?

You might come across the term 3-year Fund Volatility at the top of any fund factsheet. Here's a sample from AMB Dividend Fund factsheet:

*Note : 3 Year Fund Volatility and 3 Year Annualised Volatility are the same.

So what exactly is a 3-yr Annualised Volatility and a 3-yr Sharpe ratio?

What is Volatility?

Volatility in term of unit trust is a measure of how much the price of a fund fluctuate (go up and down) during a certain period of time. 

What is Annualised Volatility?

Annualised volatility is the measure of a unit trust price fluctuation over a period of one year.

What is 3 yr Annualised Volatility?

Measure of price fluctuation of a unit trust price over a period of 3 years.

How to calculate a 3 yr Annualised Volatility?

Normally the 3 yr Annualised Volatility of a fund is already calculated and made available for investors. However, it is important for investor to understand how the 3 yr Annualised Volatility is derived. To make things easier, I will demonstrate how a 1 yr Annualised Volatility is calculated for OSK-UOB KidSave Trust.

Calculating 1 yr Annualised Volatility for OSK-UOB KidSave Trust:

1) First step is to derive the monthly volatility for a 1 year period. In order to do this, we will need the unit trust price for every month end over a period of one year (from Jan 2012 - Dec 2012). Using the monthly unit trust prices, we are able to calculate the monthly % returns as shown in the table below:

Date	Monthly NAV	Difference between NAV (month to month)	Monthly Returns in %
31-Jan-12	0.5645
29-Feb-12	0.5774	0.0129	2.29%
30-Mar-12	0.5464	-0.0310	-5.37%
30-Apr-12	0.5514	0.0050	0.92%
31-May-12	0.5457	-0.0057	-1.03%
29-Jun-12	0.5594	0.0137	2.51%
31-Jul-12	0.5614	0.0020	0.36%
30-Aug-12	0.5764	0.0150	2.67%
28-Sep-12	0.5840	0.0076	1.32%
30-Oct-12	0.5925	0.0085	1.46%
30-Nov-12	0.5940	0.0015	0.25%
31-Dec-12	0.6114	0.0174	2.93%
*Average Monthly Returns over 1 year			0.69%
**1 Year Return in %			8.31%
* Calculated by summing up all 12 month's monthly returns and dividing the total by 12
* * Calculated by taking the Monthly NAV on 31 Dec 12 minus NAV on 31 Jan 12. The difference is divided by NAV on 31 Jan 12 after which the result is converted to %

2) From the table above, we are also able to determine:

• Average Monthly Returns over 1 year : 0.69%
• 1 Year Return in % : 8.31%

3) To calculate the monthly volatility, all we need to do is plug in the information from Item 1 and Item 2 into the formula: 

where:

• x : Monthly Returns in % from Jan 2012 till Dec 2012
• Ma : Average Monthly Returns over 1 year (0.69%)
• n : 12 (months)

4) The formula for monthly volatility would look something like this:

                            ________________________________________________

σ_{monthly volatility}  =  /(2.29% - 0.69%)² + (-5.37% - 0.69%)² +…..+ (2.93% - 0.69) ²

                                  /   --------------------------------------------------------------------------

                √                                 (12 – 1)

                        

                           =  2.25% (monthly volatility)

5) Once we have obtained the monthly volatility, we can now derived the 1 year annual volatility:

                                                                         __

σ_{annual volatility}   = σ_{monthly volatility}   X  √12

                       = 2.25% X 3.464

                       = 7.79% (1 year annual volatility for OSK-UOB KidSave Trust)

What does 7.79% Annual Volatility means?

7.79% is the calculated deviation that can happen to the annual returns (%) of OSK-UOB Kid Save Trust Fund over a period of 1 year. This deviation occurs 68.27% of the time*.

*(68.27% is an empirical fixed figure for deviation)

Earlier we calculated the 1 Year Return for OSK-UOB Kid Save Trust to be 8.31% (refer to previous table). 

In terms of volatility, the 1 Year Return for OSK-UOB Kid Save Trust will deviate between 0.52% (8.31% - 7.79%) to 16.1% (8.41% + 7.79%) at 68.27% of the time.

The actual 3 year Annualized Volatility is calculated in the same manner except that daily prices instead of monthly prices will be used for the calculation. The period for calculation is 3 years instead of 1 year.

I still do not understand how the Annual Volatility Calculation is Done!

Worry not as we do not need to understand the mathematical part of it. What's most important when you see Annual Volatility (3 year Annualized Volatility), you should be aware that:

• The higher the volatility figure, the more volatile the fund is.
• The lower the volatility figure, the lesser volatile the fund is.
• When comparing between two funds of the same category, the fund with the lower volatility will have lesser fluctuation on the unit price over a period of time.

Say two funds with the same 3 years Annualized Returns are compared in the table below:

	Eastspring Investments Asia Pacific Equity MY Fund	Pheim Asia Ex-Japan Islamic
3 Year Annualised Returns	2.20%	2.10%
3 yr Annualised Volatility	18.16%	16.48%

Both funds have almost similar annual returns of 2.10% - 2.20%. In terms of volatility, Pheim Asia Ex-Japan Islamic fund has a lower percentage as compared to Eastspring Investment Asia Pacific Equity MY Fund. While both funds are able to produce the same returns, PAEJI's fund manager is better in managing and preventing the fund price from over fluctuating!

Knowing the volatility of a unit trust fund only allows an investor to know the range of returns of that fund, it does not reflect the strength of the unit trust performance. This is where the Sharpe Ratio comes into play!

What is Sharpe Ratio?

The Sharpe ratio indicates the excess return an investor is expected to receive for every unit of risk that the unit trust undertakes.

The formula for calculating Sharpe Ratio as shown below:

Referring to the definition above, the aspect of risk and returns are the main key points here. Sharpe Ratio provides an indicator on your returns versus the risk you have taken to invest in that unit trust. 

Looking at the formula once again, you can see the "Annualised Return" is the profit you expect to make. "Annualised Volatility" is the amount of risk you are taking. When dividing profit with risk, you get a profit vs risk ratio. 

What about the term Risk Free Rate?

The risk-free rate describes the best available rate of return of a risk-free security. The interest rate of the 3-month US Treasury bill is often used as the risk-free rate but for us, using the Maybank’s 12-month Fixed Deposit rate of 3.15% as the risk-free rate is good enough.

By deducting the risk free rate from the annualised return, we now have the 'true' returns of investing in unit trust. Dividing the 'true' returns with the annualised volatility (risk taken), we have what we call the Sharpe Ratio!

It's example time!

	Kenanga Growth Fund	AMB Dividend Fund
3 Year Annualized Returns	20.80%	16.00%
3 yr Annualised Volatility	9.48%	8.01%
Sharpe Ratio	1.79	1.6

Here's a compariosn between 2 Malaysian Equity Unit Trust Fund. Kenanga Growth fund has a better 3 year annualized return albeit with higher Sharpe Ratio. AMB Dividend Fund generates a lower return and is reflected by the low Sharpe Ratio and lower volatility. Hence the saying "High risk, high returns"

Summary

Understanding about Annualised Volatility and Sharpe Ratio adds another layer of precaution when it come to investing in unit trust. In my opinion, the best time to utilize Annualised Volatility and Sharpe Ratio is when faced with the dilemma of choosing between a few funds with the same annual returns. Go for the lowest percentage volatility and the highest sharpe ratio if possible!

Cheers and Happy Investing!

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