Risk and Return for CFP-5

Modern Portfolio Theory and Asset Pricing

The relation between portfolio returns and portfolio risk was recognized by two Nobel Laureates in Economics, Harry Markowitz and William Sharpe. Harry Markowitz tuned us into the idea that investors hold portfolios of assets and therefore their concern is focused upon the portfolio return and the portfolio risk, not on the return and risk of individual assets.

The relevant risk to an investor is the portfolio’s risk, not the risk of an individual asset. If an investor considers buying an additional asset or selling an asset from the portfolio, what must be considered is how this change will affect the risk of the portfolio.

Possible Portfolio

 The Efficient Frontier: the best combinations of expected return and standard deviation.

All the assets in each portfolio, even on the frontier, have some risk. Now let’s see what happens when we add an asset with no risk—referred to as the risk-free asset.

If we look at all possible combinations of portfolios along the efficient frontier and the risk-free asset, we see that the best portfolios are no longer those along the entire length of the efficient frontier; rather, the best portfolios are now the combinations of the risk-free asset and one and only one portfolio of risky assets on the frontier.

Sharpe demonstrates that this one and only one portfolio of risky assets is the market portfolio—a portfolio that consists of all assets, with the weights of these assets being the ratio of their market value to the total market value of all assets.

If investors are all risk averse—they only take on risk if there is adequate compensation—and if they are free to invest in the risky assets as well as the risk-free asset, the best deals lie along the line that is tangent to the efficient frontier. This line is referred to as the capital market line (CML). If the portfolios along the capital market line are the best deals and are available to all investors, it follows that the returns of these risky assets will be priced to compensate investors for the risk they bear relative to that of the market portfolio.

The CML specifies the returns an investor can expect for a given level of risk. The CAPM uses this relationship between expected return and risk to describe how assets are priced.

The CAPM specifies that the return on any asset is a function of the return on a risk-free asset plus a risk premium. The return on the riskfree asset is compensation for the time value of money. The risk premium is the compensation for bearing risk. Putting these components of return together, the CAPM says:

Expected return on an asset = Expected return on a risk-free asset + Risk premium

Hence, Required rate or return = Rf + (Rm – Rf) β

Where,  (Rm – Rf) is Market Risk Premium

For each asset there is a beta. If we represent the expected return on each asset and its beta as a point on a graph and connect all the points, the result is the security market line (SML) 

Security Market Line:

Illustrations:

Find Beta of security X if expected market premium is 15%, risk free return is 7% and expected return of security X is 20%?

• (a)   0.834
• (b)   0.900
• (c)    0.700
• D)    0.867

Risk free rate of return is 8%, expected market premium is 15% and Beta of security is 0.80. What is the expected rate of return of the security?

• (a)   13.6%
• (b)   15.00%
• (c)    12.00%
• (d)   20.00%

Assume R_f  is 7%, K_m  is 16% for a security X and has a beta factor of 1.4, the required return of the security is_______.

• 21.6%
• 20.0%
• 17.4%
• 19.6%
• 23.2%

 Source: Financial Management and Analysis by FRANK J. FABOZZI.

All content belongs to FRANK J. FABOZZI.

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