How to use standard deviation to determine volatility of a portfolio

We all learned standard deviation in our statics course during high school and we have solved a lot of math questions associated with this concept in classes. But do u know that it can be used as volatility measurement of any given portfolio. It served as important indication how risky one potential investment relative to another in consideration. Let's look at two hypothetical assets with 6 years annual gains. I guess majority of investor will choose Asset B. But let us examine further and calculate the standard deviation.

Asset A with standard deviation 9.52 is expected to be able to generate annual return between 3.48 (13 - 9.52) and 22.52 (13+9.52) wheres Asset B with standard deviation 29.44,32 is expected to be able to generate annual return between -14.44 (15-29.44) and 44.44 (15+29.44) in 2/3 of the time which approximately thirteen out of every twenty years. So obviously Asset B is more risky and volatile although Asset B have bigger average return. In fact, Asset B annualized return is 11% compare to almost 13% of Asset A. Another measurement that can be used to measure volatility is risk drag which have discussed in here.

Average and Annualized Return Paradox

You have been convinced by a handsome positive average annual return as advertised in an investment instrument brochure and about to surrender your hard earned money with the hope that it will work harder for you as suggested by your agent. Wait a minute, do u have the annualized return or do u know how volatile of the portfolio?

Let's explore the table above. I listed 7 years worth of annual return data of an instrument. By summing up all the yearly figures and divided by seven, we got an average whooping 29% return. Logically, we would think this is a fruitful investment. But if you start counting from year one and starting off your journey with $10,000. By year 7, your investment only worth $3400 which is equivalent to a lost of -66% instead. Apparently the periods of loss erode value hugely, gains have to work doubly hard, first to restore the value lost and then to grow principal. If you compute the annualized gain using formula ((1 + Rate of Return)^1/N) - 1, where N is the period in years, you will get -14%. Knowing the important of calculating the annualized return or seek information of it before making decision on purchasing any investment instrument is so important,yet lot of investors choose to accept blindly the beautiful tag lines on the advertisement and recommendation by leading finance magazines is irony. Peoples need to start learning the meaning of figures or ratios being put up in the fund sheet to get self well informed. Eventually,the fist rule of investing is not to lose money.

Now you might think that average return have no reference value which is not quite true. We can use the different of annualized and the averaged to measure the portfolio volatility. The value is termed as "risk drag" .
The higher the risk drag, more volatile the portfolio.

What's the real cost of buying mutual fund?

For first time buyer, it might not be so clear what is the total long term cost being incurred when invests in mutual fund. The most prominent fee that capture attention of consumer no doubt is annual management fee. Typically in Malaysia, an equity fund commands annual management fee of 1.5% while bond fund charges a lesser fee of 1%. As a matter of fact, running a mutual fund involves costs, including shareholder transaction costs, annual trustee fee, investment advisory fees, operation fees, marketing, distribution expenses and etc. Those misc fees together with annual management fee make up the real cost of holding mutual funds. Annually this expense materializes as an expense ratio which is in nutshell merely "annual operating expenses divided by average annual net assets."

This is no way fund house is hiding this figure from investors. This figure can be obtained in their annual report and updated prospectus. The irony is investors more interested in the yearly gain instead of figures being shown in balance sheet and new buyers are often sold to newly launched funds. This ratio need at least a year worth of data to compute.

So why does it matter? Well if under same fund category, it serve as a factor to take into consideration to choose a fund to invest in. The one with higher MER will erode more of your yearly gain and the fund manager in fact need to work harder to beat the index to justify the asking price.