Under- and Over-valued Assets: Homework Help

Under- and Over-valued Assets:

If individual assets and portfolios are priced correctly, they lie exactly on the SML. Assets plotting off the SMI, indicate misprinting of assets by the market, Assets that plot above the SML are undervalued. They offer higher expected return than assets of a similar risk class. Hence, they are attractive. The buying pressure for such assets will. push up their price and lower the return, until they arc correctly priced. Similarly, assets that plot below are unattractive because they are overpriced.

In a well functioning market, an investor can obtain the fair return' predicted by the SML for a given risk by mixing the risk-free asset and the market portfolio in the right proportions. Suppose, an investor expects that stock X with beta 0.5 would yield return of 6 per cent. If the risk-free rate : is 5 per cent and the market risk premium is 6 per cent. the required rate of return is 8 per cent (5 '" 0.5 x 6 = 5 '" 3). Clearly. the stock is overpriced. The obtain SML indicated return of tr per cent by mixing the risk-free asset and the market portfolio in equal proportions to create a portfolio that has beta of a mixture of risk-free and the market portfolio? The reason is that. these opportunistic are available to all investors. The only way to create beta 0.; is to mix the two curricular» In equal proportion. As the expected return on the market portfolio is 11 per cent is the expected return on the new portfolio would be 8 per cent (= 0'; x 5 .• 0.5 x 11).

Let us take another example. the investor expect' 1'5 per cent return on stock Y. which has a beta of 2. This time the SML determined required rare is 17 per cent. Again, the stock is overvalued. The investor can still earn 17 per cent by creating a leveraged portfolio with a J:>etaof 2. For this, the investor needs to borrow funds equal to his owned funds and invest the! entire -arnount in the market portfolio. The beta of this portfolio is 2 ( = -1 x 0 + 2 x 1). The expected return is 17 per cent (= -1 x 5 + 2 x II). Thus, when defensive stock is overvalued, the investor should combine market portfolio with lending (risk-free asset). When aggressive stock is overvalued, he should combine market portfolio with borrowing.

The vertical distance between the fair return predicted by the SML, and return actually expected by an investor is called the alpha (n) of the asset. Thus, undervalued assets have a positive alpha, and overvalued assets have a negative alpha. For example, if the risk-free rate is 5 per cent and market return is expected to'be 15 per cent. fair return. stipulated by the CAPM. on a security with beta of 1.2 will be 23 per cent. If a person expects the return to be 25 per cent, the implied alpha is 2 per cent. The security is undervalued and attractive. If the security is expected to return 20 per cent. the alpha is negative at 3 per cent. the security is mispriced and overvalued. The essence of security analysis is to search for securities with positive alpha. In practice. minor deviations on both sides of the SML indicate the effect of transaction costs and taxes. Besides. due to imperfect information. investors fail to notice these opportunities and prices hover around their equilibrium level. Thus. SML is more of a band than a precise relationship between beta and the expected rate of return.

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RISK AND RETURN

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