## Tuesday, July 31, 2012

### Making Investment Decisions Based on Data, Part 1: The Sharpe Ratio

PERSONAL FINANCE 101

We have learned from several past posts (like this) that returns and risk are two of the most important factors (some say the only factors) that investors should consider in evaluating available investment instruments. Returns are funds in excess of the invested amount (e.g., dividends, capital gains, interest) received by investors at some future date; the percentage return of an investment is the return divided by the invested amount. Risk is defined in many ways, most often as the chance for an investment loss or the volatility of investment returns and is commonly measured using statistics like variance or standard deviation. In this post and the next, I will show you how to apply these concepts on actual data and choose between investment alternatives objectively.

Computing for expected return and risk

The first step, of course, is to actually get data. I've looked long and hard for "free" sources of historical UITF NAVPUs, to no avail. Then I asked one of our readers, Max (who asked a question via email about asset allocation) if she could ask for historical NAVPUs from BDO, with whom she has a UITF account. BDO did give her historical daily NAVPUs of their equity and fixed income funds, but these came in the form of screen caps so I spent a good part of the day typing the data into Excel. I am now verifying with my contacts from BDO and BPI if they can provide current and potential clients with historical NAVPUs to perform data analysis with. And while we're waiting for their response, I guess this typed-in data set will have to do (download this Google spreadsheet as an Excel file).

Then, prepare the data by computing for the percent change in daily NAVPU. Divide the NAVPU on a particular day by the NAVPU of the previous day; do this to both funds on all days (except on the earliest date, January 2, 2012).

We get the expected return of each fund by computing for the geometric mean (we have learned from this post that it's more appropriate to use the geometric mean than the arithmetic mean for investment returns), for which we can use the GEOMEAN() function of Excel. For risk, we compute for the standard deviation of the daily % changes using the STDEVP() function. The results you get should be as follows (subtract one from the GEOMEAN results and apply the percentage format to all numbers):

 Equity fund Fixed income fund Expected return 0.1234% 0.0211% Risk (standard deviation) 0.9444% 0.1414%

If you can choose to invest in only one of these two funds, which would you choose? While the equity fund has a higher expected return than the fixed income fund, its higher standard deviation indicates a greater possibility for a loss. This relationship illustrates the trade off between return and risk.

The Sharpe Ratio

To be able to evaluate the funds objectively taking in both return and risk, we can use a simple form of the Sharpe Ratio (named after William Sharpe, a Nobel Prize-winning economist and one of the proponents of the Capital Asset Pricing Model), which essentially just measures return for every unit of risk. In our example, we get the Sharpe Ratio by dividing the expected return of each fund by the standard deviation; intuitively, the investment with the higher Sharpe Ratio--the one with the "bigger bang for the buck"--is better. So which fund is it?

So far, we have seen how we can use data in choosing between two investment alternatives, taking both expected return and risk into consideration. Some of you may have noticed that this situation is simplified since it's always possible to invest in both funds simultaneously. In the next post, we will explore how we can use the data that we have and some of the concepts we have learned in this and prior posts to construct an "optimal portfolio"--the best combination of the two funds that may even be better than each individual fund, all thanks to the magic of diversification.

UPDATE 10:12 PM

My friend from BPI Trust kindly pointed out that historical prices of BPI funds as far back as 2005 are available on their website. You can try applying the procedure discussed in this post to some of BPI's funds. Since as rule bigger data sets lead to more reliable results, in Part 2 I will instead use BPI's data to illustrate optimal portfolio allocation.

UPDATE 02 AUG 2012

UITF.com.ph is a more complete source of historical NAVPUs. Thanks to reader Ace for sharing this with us.