Alpha (a.k.a. Jensen’s Alpha) is a risk-adjusted performance measure on an actual portfolio return (Rp) relative to its expected return (benchmark RB). Positive Alpha means the portfolio outperformed its benchmark and vice versa. In other words, Alpha tells us how much a portfolio beats its benchmark, and thus it’s often used to measure how well a mutual fund manager performs. Simply speaking,
Alpha = Rp – RB ……………………………….(1)
Usually, we’d take market as our benchmark. The most popular way to estimate the benchmark return is through the use of Capital Asset Pricing Model (CAPM):
RB = Rf + Beta * (Rmkt – Rf) ……………………………….(2)
where Rf = Risk-free Rate, Rmkt = Expected Market Return, and Beta = Systematic Risk (a.k.a. market risk or undiversifiable risk). (Rmkt – Rf) is known as Market Risk Premium.
CAPM assumes the portfolio is well-diversified eliminating any unsystematic risk (i.e. company-specific risk) and leaving only systematic risk. Systematic risk, Beta, is the sensitivity of the expected portfolio return (RB) to the expected market return (Rmkt). One way to estimate Beta is to regress historical portfolio returns against historical market (e.g. Hang Seng Index) returns. The slope of such regressed line is Beta. The greater the correlation coefficient between the two returns indicates a stronger linear relationship and a more reliable Beta.
A positive return with high Beta means a return following a positive market return. Beta that is greater than one is simply a leverage on market return. If there was a downturn in the market, a high Beta could cause severe loss to the portfolio. That’s why Beta is called market risk.
Combining equations (1) and (2),Watch Full Movie Online Streaming Online and Download
Alpha = Rp – [Rf + Beta * (Rmkt – Rf)] ……………………(3)
As we can see, Alpha is actually the return in excess of the reward for the market risk. A positive return with high Alpha implies a high fund manager’s stock screening ability as the actual portfolio return depends less on the market.
Let’s take an example. Suppose our stock portfolio has an actual annual return of 15%. With reference to the Hong Kong 10-year government bond’s average rate, risk-free rate is equal to about 1% per annum. If market risk premium (Rmkt – Rf) and Beta equal 9% and 1 respectively. By applying equation (3), Alpha is 15% – (1% + 1*9%) = 5%, which has outperformed the market by 5%. However, if Beta equals 2, Alpha becomes -4%. In this case the portfolio has underperformed the market by 4%, even though the actual annual return is positive.
With the aid of Alpha Investments* Statistics Webpage, it’s very easy to determine the portfolio Beta of stocks that are traded in Hong Kong market. Stock Beta is computed as stock returns are regressed against HSI returns. For instance, suppose our portfolio consists of stocks shown in the following table. After retrieving each stock Beta from Alpha Investments Stats page, we can calculate the portfolio Beta as the weighted sum of stock Beta. With the actual portfolio return and the value of portfolio Beta on hand, we can estimate Alpha performance of our portfolio and see how well we actively manage our portfolio from time to time.
|Stock||Beta#||Weight||Beta * Weight|
|CHEUNG KONG 長江實業 (00001.HK)||1.07||30%||0.321|
|YUEXIU PROPERTY 越秀地產 (00123.HK)||1.46||15%||0.219|
|CCB 建設銀行 (00939.HK)||1.09||20%||0.218|
|CHINA MOBILE 中國移動 (00941.HK)||0.88||15%||0.132|
|CHINA LIFE 中國人壽 (02628.HK)||1.18||20%||0.236|
|#Beta values were taken as at 18Oct2012||Portfolio Beta||1.126|
*Alpha Investments (English: http://alphainvestments.hk/en/ ;Chinese: http://alphainvestments.hk) is a website dedicated to analyze historical investment data for the Hong Kong market. It provides an intuitive platform for market participants to use to identify potential trends from pricing and volume history, and therefore, to seek Alpha.