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Archive for April, 2007

Do Fund Managers Beat The Market?

Published April 27th, 2007 in Finance. 0 Comments

Seeking alpha

Back in 1969, Jensen has studied the performance of 115 funds for 10 years. He calculated the difference between the return of the funds minus the expected return of the fund, according to the CAPM model. Jensen has computed what is known as the alpha of the funds:

R_i-R_f = \alpha +\beta(R_m-R_f)

From that research, this “alpha” has been given the name the Jensen Index. The research showed that 50.4% of the funds that have achieved a positive alpha, had achieved in the following year a positive alpha.


wilshire.jpg

The picture above shows the percentage of funds that have achieved lower returns than the Wilshire 500 index.

Another research by Frank Russel Co. showed that out of a sample of 100 private fund managers, those who have achieved better returns than other funds for a certain period (83-86), were not able to do so in the following period (87-90).

The above research shows the inconsistencies in returns by funds which go along with the notion of an efficient market.

Is it worthwhile to invest in stocks?

There is a problem here. If fund managers can’t translate stock analysis to outperform the market, then they won’t invest in the first hand in analyzing the stocks. If all managers do so, the prices of stocks will not reflect their fair price and it will be again worth while to analyze the stocks! This means there is an equilibrium point where a handful of fund managers do invest the time to analyze earning reports and are compensated with returns.

The conclusion for the small investor

Big funds have lower costs of fundamental analysis than the small investor. Hence he will be better off buying a passive investment such as the market index.

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How To Compare The Performance of Funds - Part II

Published April 23rd, 2007 in Finance. 0 Comments

In the last post, I wrote about the different methods in comparing performance of funds. I have assumed the investor is indifferent to risk. The only question the investor had asked himself was “Who will give me the best expected returns?”

What if the investor asks “Who will give me the best expected return for a given risk?” That is an entirely different question. Mathematically, it looks like this:

Max:\left(\frac{E(R_i) - R_f}{\sigma_i}\right)

Where E(R_i) is the expected return on the investment, R_f is the risk free rate and \sigma_i is the volatility of the investment. Note: The above is better understood when you have the basic idea of the CAPM down. You can either google it, or wait for me to write about it which I plan in the future. The above formula is known as the Sharpe Ratio. The theory is that investors want to maximize the above equation.

The Sharpe ratio can tells us which fund had a better performance. We can also compute the sharpe ratio of the market (we can pick the S$P500 for instance). The sharpe ration of the market is the bench mark to beat. If the sharpe ration of the fund was lower than the sharpe ratio of the market, the fund did poorly.

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How To Compare The Performance Of Funds - Part I

Published April 19th, 2007 in Finance. 1 Comment

In this post, I’ll try to explain the different methods to assess the performance of fund managers. How do you choose a fund? If you, the investor, is risk indifferent, you would probably choose the fund that has the biggest return expectancy. How do you calculate the expected return?

Let’s assume you are to choose between two fund managers, and you collect the historical returns of the last four years:

2002 2003 2004 2005

10% -20% 15% 5% : A

-5% 10% 25% 0% : B

Which fund would you choose? If we assume that past performance implies future performance (which will be discussed later), it depends on how we calculate the mean. We could choose to calculate with either arithmetic mean or geometric mean.

For the arithmetic mean:

R_a = \frac{10%-20%+15%+5%}{4} = \frac{10%}{4} = 2.5%

For the second fund:

R_b = \frac{-5%-10%+25%+0%}{4}=\frac{10%}{4} = 2.5%

According to the arithmetic mean, both funds achieve the same mean, hence we should be indifferent in choosing any of which.

Let’s examine now the geometric mean:

(1+R_a)^4 = 1.10\cdot 0.8\cdot 1.15\cdot 1.05 => R_a = 1.53%

The geometric mean for the second fund is:

(1+R_b)^4 = 0.95\cdot 0.9\cdot 1.25\cdot 1.00 => R_b = 1.67%

According to the geometric mean, the second fund achieved higher mean. The question is now, which method is better then?

Here is a rule of thumb: The geometric mean is always lower then the arithmetic mean. Moreover, the bigger the volatility of returns, the lower the geometric mean would be. Now we know why the first fund had lower returns than the second fund. Since both funds achieved the same arithmetic mean, we expect that both geometric means would be lower than the arithmetic mean. But since the first fund had more volatile returns, it has a lower mean.

We still haven’t answered which way is more “correct”. Let’s take a practical view. Suppose we had invested 100,000$ in both funds four years ago. What would be our compounded returns?

For the first fund, the way to calculate it would be

1 + R_a = 1.10\cdot 0.8\cdot 1.15\cdot 1.05 => R_a = 6.26%

For the second fund:

1+R_b = 0.95\cdot 0.9\cdot 1.25\cdot 1.00 => R_b = 6.87%

Notice that this method is essentially the same as computing a geometric mean. This means that if you had invested in the second fund four years ago, and cashed out after four years, you would receive a bigger return than in the first fund!

It is tempting to conclude now that the geometric mean is the way to go isn’t it? But let’s assume that we change our investment policy. Suppose you invest an initial sum of 100,00$ but now if after one year the fund achieved a positive return, you cash out the return, and if it is a negative return, you add enough money to update the sum to 100,000$ again. At the end of 4 years, you cash out. What is the return in this case?

This means we have to the IRR of such an investment.

For the first fund, the calculation yield a IRR of 2.44%, while for the second, a IRR of 2.35%. Going back to the original question, which fund manager would you choose for a future investment? If we assume that there is no correlation between returns in each year, meaning that the order of returns doesn’t matter, using the arithmetic mean is a valid method. This means that both funds achieved 2.5% and hence we would be indifferent between them.

If you ask though the question who got better returns in the past, it depends in which method. In the first one, when the investor put the money for four years and cashed it out only at the end? or the second one who either cashed out each year or updated the sum to match the initial investment.

If you notice, we haven’t discussed the topic of risk. That is to come in the second part.

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