Investment –How to Allocate Money into Equities

Hi there.

As the investment manager always says, the most crucial step on divvying money into investment market has been how much fraction of money should be put between risky assets. Now I would like to initiate discussion –practical guidance on how to invest money into the equity market.

In this discussion, the primary objective is the highest return on investment in the long term of investment period. Furthermore, it is how to achieve optimum return while maintain minimum risk (and apparently this is the most celebrated Sharpe ratio) using historical return data from the past. This would be a naive structure of analysis and hence discussions are appreciated. I would leave the exact definition of long term for discussion.

Commonly, the first step is a qualitative evaluation to select what equity should be purchased. I would like to skip the evaluation and give the already chosen equities. The figure below shows the relation between index return of Bursa Efek Jakarta (horizontal axis) and equity return of each company (vertical axis), comprises of data from January to September 2013.

Five equities are hence selected for the risky portfolio from a broad of industries, i.e.: Inco (INCO), Unilever (UNVR), Astra International (ASII), Tambang Batu Bara Bukit Asam (PTBA), and Bank Rakyat Indonesia (BBRI). These are all listed in Bursa Efek Jakarta. It is apparent that return of ASII is very positive sensitive to the dynamic of return of the market while its risk is very low –represented by distribution of the return points that are close to the trend line. At the other side, dynamic of return of INCO is slightly negative to the dynamic of return of the market while its risk is very high –distribution of the return points is spread away from trend line. Preliminary suggestion would advise that investor should put the money away from INCO and PTBA as the risks are very high!

Statistic values extracted from the historical data of market and equity return and used for our analysis are as follows.

Variable beta represents sensitivity of equity return and market return. Variable alpha represents how much equity returns while the market return is zero. Two other important statistic variables are residual variance and residual sum of squares. It is noteworthy the “i” denotes individual equity and “p” denotes collection of equity or the portfolio.

Technical assumption and constraint for finding optimal money allocation are as follow.

1. It is assumed that short-sale is prohibited. Thus, allocation would not be negative,
2. All money shall be invested into five equities. Thus, sum of the fraction of allocation is 1, and
3. Minimum allocation is 1% of total money

Statistic values of portfolio are calculated as follow,

1. Alpha p: sum of product of Alpha i and its allocation
2. Beta p: sum of product of Beta i and its allocation
3. Residual value p: sum of product of residual value i and square of its allocation
4. Return p: alpha p + beta p * (expected return of market)

Adjusted variable is calculated as follow,

1. Standard deviation p: square-root of (variance of market return * square of Beta p + residual value p)

And objective variable is calculated as follow

1. Sharpe ratio p: return of portfolio divided by its standard deviation

Using Excel spreadsheet, these four aspects are workable using Solver module.

Now, the procedure for calculations is

1. Formulate assumptions, constraints, and calculations mentioned previously into spreadsheet,
2. Set the equity weight wi 0% for INCO, UNVR, BBRI, ASII and leaves PTBA 100% allocation,
3. In the Solver module, set the target value to maximize Return portfolio, by changing values of equity allocation and subject to the assumptions and constraints, minimum allocation of 1%, sum of allocation is 100%, and portfolio standard deviation is 0.017. Don’t forget to click “Solve” button.
4. Excel will then provide you with the result of each equity allocation. Write down the resulted expected return of portfolio paired with the standard deviation of portfolio

Repeat the procedure for another value of portfolio standard deviation and the corresponding portfolio return would be such this figure below

The blue line is one of the most well-known curve in the theory of investment; efficient frontier made famous by Markowitz. The line represents a set of maximum expected return that would yield from specific allocation into risky assets for each value of risk (represented by standard deviation) an investor are willing to take.

As with our main objective, the highest Sharpe ratio is indicated by red dot from the efficient frontier line above. With a 0.016 standard deviation, the maximum expected return from portfolio would be 0.3%. It means 0.178 Sharpe ratio. And this also relates to the following allocation of money.

From the table, INCO and PTBA were historically poor performer. Meanwhile, more than two-third of money should be invested into BBRI.

Now is for the practical consideration. Equity selection involves qualitative analysis of how is the company business plan, who is the CEO and its management team, etc. Thus, it should be long-term activity.

Dive into more frequent activity, as the equity price of a company is changing rapidly; the money allocation should also change over time to keep the Sharpe ratio maximum. Therefore, investment manager should frequently extract historical data and initiate the calculation procedure. With a certain amount of subscription fee, Bloomberg provides an add-on to simplify data extraction into spreadsheet. Thus, calculation for money allocation could be scheduled for each week or even each hour.

Note: please find spreadsheet of calculation here. And as always, discussion are welcome.