Capital Allocation and Capital Market Line
Capital Allocation Line (CAL):
Asset allocation is the allocation of funds across different types of assets that have variable degrees of expected risk and return levels, whereas capital allocation is the allocation of funds between risk-free assets and risky assets. The CAL represents the set of all possible combinations of risky and risk-free assets for investment. The graph is representative of the return that an investor is likely to get given the level of risk that the investment incurs by combining the risky and risk-free assets. The line begins at a point where the percentage of the risky assets is zero and extends to a point where the risk percentage is 100%. The risk associated with an asset is measured in terms of its standard deviation. The slope of the CAL is known as the Sharpe’s Ratio. The greater the Sharpe’s Ratio, the better is the risk-adjusted-performance of the portfolio.
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E(rp) = The expected rate of return of the portfolio.
rf = Risk-free return
S = Sharpe Ratio
σ = Standard deviation (%Risk)
The CAL is used in selecting an optimal portfolio for an investor. The intersection of the Efficient Frontier, which is a set of all efficient portfolios, and the CAL gives the most optimum portfolio i.e. a portfolio that has maximum utility.
Capital Market Line (CML):
The Capital Market Line is a special case of the Capital Allocation Line. The risk portfolio in the CML is the market portfolio and hence the name Capital Market Line. The slope of CML is the Sharpe Ratio of the market portfolio.
Example problem: Investing with the CML
Given data:
Solution:
Given our understanding of the CAL and CML, the portfolio with the greatest Sharpe Ratio gives the best risk-adjusted-performance.
In this case, the portfolio 3 gives a maximum of 0.500 units of expected risk premium per unit of risk. Thus, this portfolio should be considered as the best market portfolio.
Now Suppose = the investor is willing to assume a standard deviation until 8.5%.
From the CML equation, corresponding expected rate of return with portfolio 3 would be
Rp = 4.00 + 8.500*0.500
= 8.25%
We can see clearly that there is no way to achieve this rate of return with the given portfolio. The strategy that can be employed to achieve this amount of return at the given risk could be diversification of the portfolio.
This can be solved as under:
8.25% = (Risk-free asset) * 4% + (1- (Risk-free asset)) * 9%
This gives Risk-free Asset = 0.15
This means that the investor should invest 15 percent of his funds in the riskless asset and the remaining 85 percent in Portfolio 3.
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Difference between The Capital Market Line and the Security Market Line:
| Capital Market Line | Security Market Line |
| 1. Shows the rates of return for a given portfolio. | 1. Shows the expected return of individual assets. |
| 2. The measure of risk is the standard deviation of returns. | 2. The measure of risk is systematic risk or beta. |
Author: Abhay Kanodia
About the author: An undergraduate student from the Birla Institute of Technology and Sciences, Pilani(BITS Pilani). Exploring the fields of finance and data analytics and its applications in other different domains.
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