Calculating expected return on investment using Capital Asset Pricing Model
Calculating expected return on investment using Capital Asset Pricing Model
Introduction:
In a valuation exercise, the discounting factor (derived from the expected rate of return) is of crucial importance. There have been numerous discussions and debates on the approach to arrive upon this discounting factor. From predominantly relying on “instinct” to the new generation of scientific models, there has been a multitude of thoughts to arrive upon one “appropriate methodology”. The earlier edition described in detail the various methodologies which have evolved in this domain. A conclusion was drawn on the practicality and efficacy of Capital Asset Pricing Model (CAPM) over other models.
This paper explores the practical issues in arriving at the discounting factor using Capital Asset Pricing Model. There is a conscious effort to examine the availability of appropriate data to be used in the model from the Indian perspective. To facilitate such critical examination, a past case has been selected from the universe of valuations conducted by Haribhakti Group. The names and details have been appropriately changed keeping in mind the client confidentiality requirements.
Background of the company:
The company is engaged in the business of manufacturing and exports of gems and studded jewellery. It has extended its operations in more than 10 countries like US, Japan, Hong Kong etc. The company has further ventured into international retail market, by setting up retail chain stores at various locations.
Purpose of valuation:
The company was in the process of acquiring shares of overseas companies for the purpose of consolidation.
As discussed earlier, the Capital Asset Pricing Model (CAPM) is the most preferred risk/return model. Therefore, the expected rate of return of the stock selected can be calculated as:
Expected return on investment = Risk free rate + Beta * (Market return - Risk free rate)
A cursory glance at the model would give a perception that application is straightforward. However, the choice of input data (e.g., whether the risk free rate to be considered should be 1 year or 5 years or any other term) could alter the end result substantially. As a practitioner of valuation, the key issues which lead to a choice of particular factor have been examined in detail.
These factors are:
1. Risk free rate 2. Beta 3. Risk Premium (Market return – risk free rate)
1. Risk free rate:
The valuation of the company selected was undertaken under the going concern assumption, which is based primarily on the future expected cash flows which the company generates. These cash flows were projected over a time spectrum, and discounted to the present values using the discounting factor. The present values were aggregated to arrive on the value of business.
It is thus rational to use different discounting rate for cash flows of different period, as the yield curve is never flat across the time horizon. However, it is not practical to match the relevant interest rates to the time period of the cash flows. An alternative to overcome this issue is to compute the duration of the cash flows, and use the corresponding rate for calculation.
Fundamentally, for an investment to be risk free in nature there should be no default risk. The Government securities of most countries are default free in nature. Therefore, the risk free rate is essentially the yield on the Government bond, and forms the base of this model.
The 9.39% GOI 2011 is priced at Rs 106.95/- thereby yielding 7.69% (as on 30th June, 2006). Source: nseindia.com
Beta of the investment:
Beta is not a measure of volatility as often described to be; rather it is the responsiveness of the stock to the market. Thus a stock with high volatility can have low beta, or a stock with low volatility to have high beta. This is because a stock can be highly volatile, but so could the market, and therefore have a low beta.
Beta of an asset = Covariance of asset with market portfolio ------Variance of the market portfolio
To calculate the beta of the stock, it was important, not only to select a broad based index, but also an appropriate time period for consideration. The covariance of the stock was derived from the historical closing price. A six year historic price movements of the stock was considered to calculate the covariance of the stock with the market portfolio.
The CAPM describes the market portfolio as having each and every asset which is traded in the market. Therefore, in order to calculate the variance of the market portfolio, a broad based, diversified index should be considered. However, if there is a sector specific index for the stock e.g., BSE-Teck index, then it would be appropriate to consider it as the market portfolio. This is because the broader market may have delivered 20% returns over a certain period of time, but the sectoral index could have outperformed the market in a big way. So going forward, the investor may expect a higher return from say a technology stock, than the returns from the market.
Due to the absence of a Gems and Jewellery index, the S&P CNX 500 was considered as the market portfolio. This is because the index not only includes a large number of companies in various sectors of the economy, but also represents about 92% of total market capitalization. The closing rates of the index over the last six years were considered to find the variance of the market portfolio. In emerging markets like India, it is important not to go back too much in time. Since the markets are so susceptible to change, that it would not give a fair picture.
Stock price and Index movements
Time Period Stock Price S&P CNX 500 Index
3-Jan-00 101.5 1,291.6 1-Jan-01 45.0 907.8 1-Jan-02 20.8 698.9 1-Jan-03 23.5 777.2 1-Jan-04 62.1 1,563.0 3-Jan-05 94.6 1,834.8 2-Jan-06 402.5 2,464.3
Beta of stock = 0.000165 ------= 0.53 0.000309
Risk premium:
It is the premium that an investor would demand for investing in equities as an asset class as opposed to the risk free investment. If an investor can earn 8% returns by investing in a G-sec, it is natural to demand a higher return for investing in a riskier asset. This premium is essentially the excess of market return over the risk free rate.
Market return is derived from the historical returns observed for similar asset class or the broad market. As explained earlier S&P CNX 500 has been considered as a similar asset class. For calculating the market return, the average daily returns of S&P CNX 500 over the last 6 years were computed. These daily returns were then annualized (average daily return * 365).
Bringing this together CAPM was used to estimate the expected return on a stock for the future.
Risk free rate = 7.69% (yield on GOI 2011) Beta of stock selected = 0.53 Risk premium = 20.43% (6 year returns of S&P CNX 500)
Expected rate of return of stock selected = 7.69 + 0.534 (20.43-7.69) = 14.49%
Even though statistical studies have proven that CAPM essentially explains only about 7% of the stock price movements, it is still favored over the other models. While both the Arbitrage Pricing model and the Multi- factor model do great work at explaining differences in past returns, as they do not restrict themselves to one factor, as CAPM does. However, this extension to multi factors makes both the models complex and impractical to use in the real world.
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