Some, but not all, of the risk associated with a risky investment can be eliminated by diversification. The reason is that unsystematic risks, which are unique to individual assets, tend to wash out in a large portfolio, but systematic risks, which affect all of the assets in a portfolio to some extent, do not.

Because unsystematic risk can be freely eliminated by diversification, the systematic risk principle states that the reward for bearing risk depends only on the level of systematic risk. The level of systematic risk in a particular asset, relative to average, is given by the beta of that asset.

The reward-to-risk ratio for Asset i is the ratio of its risk premium, E(Ri) – Rf, to its beta, Bi: [E(Ri) – Rf]/Bi

In a well-functioning market, this ratio is the same for every asset. As a result, when asset expected returns are plotted against asset betas, all assets plot on the same straight line, called the security market line (SML).

From the SML, the expected return on Asset i can be written: E(Ri) = Rf +Bi[E(Rm) – Rf]

This is the capital asset pricing model (CAPM). The expected return on a risky asset thus has three components. The first is the pure time value of money (Rf), the second is the market risk premium, [E(Rm) – Rf], and the third is the beta for that asset, Bi.

The CAPM implies that the risk premium on any individual asset or portfolio is the product of the risk premium of the market portfolio and the asset’s beta.

The CAPM assumes investors are rational single-period planners who agree on a common input list from security analysis and seek mean-variance optimal portfolios.

The CAPM assumes ideal security markets in the sense that: (a) markets are large, and investors are price takers, (b) there are no taxes or transaction costs, (c) all risky assets are publicly traded, and (d) any amount can be borrowed and lent at a fixed, risk-free rate. These assumptions mean that all investors will hold identical risky portfolios.

The CAPM implies that, in equilibrium, the market portfolio is the unique mean-variance efficient tangency portfolio, which indicates that a passive strategy is efficient.

The market portfolio is a value-weighted portfolio. Each security is held in a proportion equal to its market value divided by the total market value of all securities. The risk premium on the market portfolio is. proportional to its variance and to the risk aversion of the average investor.

In a single-index security market, once an index is specified, any security beta can be estimated from a regression of the security’s excess return on the index’s excess return.

This regression line is called the security characteristic line (SCL). The intercept of the SCL, called alpha, represents the average excess return on the security when the index excess return is zero. The CAPM implies that alphas should be zero.

Estimates of beta from past data often are adjusted when used to assess required future returns.

THE ARBITRAGE PRICING THEORY

An arbitrage opportunity arises when the disparity between two or more security prices enables investors to construct a zero net investment portfolio that will yield a sure profit. Rational investors will want to take infinitely large positions in arbitrage portfolios regardless of their degree of risk aversion.

The presence of arbitrage opportunities and the resulting volume of trades will create pressure on security prices that will persist until prices reach levels that preclude arbitrage. Only a few investors need to become aware of arbitrage opportunities to trigger this process because of the large volume of trades in which they will engage.

When securities are priced so that there are no arbitrage opportunities, the market satisfies the no-arbitrage condition. Price relationships that satisfy the no-arbitrage condition are important because we expect them to hold in real-world markets.

Portfolios are called well diversified if they include a large number of securities in such proportions that the residual risk or diversifiable of the portfolio is negligible.

In a single-factor security market, all well-diversified portfolios must satisfy the expected return-beta relationship of the SML in order to satisfy the no-arbitrage condition.

If all well-diversified portfolios satisfy the expected return-beta relationship, then all but a small number of securities also must satisfy this relationship.

The APT implies the same expected return-beta relationship as the CAPM yet does not require that all investors be mean-variance optimizers. The price of this generality is that the APT does not guarantee this relationship for all securities at all times.

A multifactor APT generalizes the single-factor model to accommodate several sources of influence on a stock’s expected return

Case Back Ground

MRPL was the first Grass root refinery of India with a capacity of 3 mmtpa. It started its operations in 1996 at a cost of Rs.25.93 Billion. The capacity of the project was increased to 9mmtpa at a additional cost of Rs.37 billion in 1999.In initial year of operation the company made aprofits however 1999-2000 onwards it started turning red.The companies debt to networth ratio rose from 5.61 in 1999-00 to 16.13 in 2001-02.

RPL started operations in 2000-01.It was the largest private sector company in terms of sales during 2000-01.The performance of the company was very good compared to MRPL and other public sector companies. The structure of debt and operational efficiency were the hallmark of the company. The good corporate financial practices resulted into lower initial project cost which gives an advantage in operational years.

Problems in the Case

MRPL

High production cost

High debt and interest burden

Low capacity utilization

Decreasing stock price

Rising losses

Increasing crude oil prices

RPL

Government regulations RPL looses about 550 Cr. in 2000 due to export

Increasing crude oil prices

Question-1

The per ton cost of RPL project was 30 % less than the MRPL project cost .The cost of funds for MRPL was also very high 16 % and 17.5 % respectively for secured redeemable PCD and SR CD. The high cost of debt leads to very high interest burden on MRPL. The effective payout on TOCD is much lesser leading to lesser interest burden on RPL .The interest burden per MMT of refining capacity for MRPL was Rs.747 Million whereas the same for RPL was Rs. 354 million. The capacity utilization of MRPL is also low (93.5 % in 1996-07) whereas RPL ‘s capacity utilization was 100 % in the first year of operation (2000-01) .The under capacity utilization increases the fixed cost component of the finished product and it results to lower profit margin.

The RPL also has economy of scale advantage as the capacity of the project is 27 MMTPA in comparison to MRPL 9 MMTPA.

The RPL has backward integration i.e. the final or by product of one process is feed stock for another process which gives RPL a cost advantage.

From exhibit-III it is observed that RPL has highest PAT followed by BPCL ,HPCL, CPCL. MRPL made losses amoun6ing to Rs. 4924.79 in 2001-2002.RPL has highest net profit margin during the year 2000-01 and 2001-02 followed by BPCL, HPCL and CPCL.

P/E ratio is highest for RPL followed by BPCL,HPCL and CPCL.P/E ratio indicates that the stock of RPL is highly priced compared to earnings per share. The high P/E ratio can be because of high perceived value of the share by the investors or high expected returns in future. High P/E ratio also indicates positive sentiments of the investors towards stock .However sometimes speculative news can also contribute to increase in share price. High P/E ratio of RPL is because of low EPS in 2000-01.EPS is highest for BPCL followed by HPCL and CPCL.

Question -2

Beta of a stock tells about response of the stock price to market sentiments or systematic risk. Systematic risk refers to a condition which in general affects all stocks, for example inflation, GDP and interest rate. A stock may have negative or positive beta coefficient. The magnitude of beta gives an indication how great an impact a systematic risk has on a stock’s return. For example if two stocks have beta of 2 and 3, this implies that second stock is more responsive to fluctuation in risk factor compared to first one. Or the second stock is more risky than the first one. A positive beta means that the return will rise or fall with the increase or decrease in market risk.

Beta for RPL and MRPL are calculated taking three months periodicity .The calculations are shown in exhibit-1

From Exhibit-I

Beta for RPL=0.9971

Beta for MRPL=0.012

From above equations it can be inferred that RPL stock is more risky than MRPL.

Required rate of return for RPL will be 7.5+0.997*11.17= 18.36%

Required rate of return for MRPL 7.5 +0..088*11.17= 8.5 %

EXPECTED RETURN FOR RPL AS WELL AS FOR MRPL LIES WITHIN Μ ± STD. DEVIATION .HENCE 68. 3 % TIMES INVESTORS CAN BE CONFIDENT OF THE RETURNS.

QUESTION-3

( From exhibit-II)

Average return on RPL and MRPL shares is 4.7 % and -2.7 % respectively. The risk for the same will be 11.17-4.7 and 11.17-(-2.7) i.e. 6.47 % and 14.47 % respectively.

The systematic risk for RPL=.9971*6.47= 99.7 % of total risk

Unsystematic risk for RPL=6.47-6.45=0.024 = 0.3 % of total risk

The systematic risk for MRPL=0.0127*14.47=4.06 = 0.01% of total risk

Unsystematic risk for MRPL=14.47-0.01=14.46 = 99.9 % of total risk

Question-4

Return and risk are shown in exhibit-III and Exhibit-IV .The efficient frontier for the portfolio is also shown in the graph.We observe that as proportion of MRPL share goes up the risk goes down till 50 % However risk started increasing as MRPL share goes above 50 %. 50 % RPL and 50 % MRPL stock portfolio has the minimum variance. The portfolio risk based on weighted average of individual stocks in much higher (Exhibit-IV) and it goes up as MRPL share goes up. However in case of port folio risk the unsystematic risk both get cancelled out.Hence overall risk is less of a portfolio than a single stock.

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