Todd Karabon, a junior analyst for investment boutique Marsh & Sons, has just been assigned his first security-analysis project. Before he starts crunching numbers, Karabon decides to review his portfolio theory.
Karabon starts with a look at capital market theory. He remembers that the theory requires a number of assumptions, and he jots some of them down:
- Every investor has the same time horizon.
- Investors can borrow at the risk-free rate and know in advance about their real cash flows.
- All investors make investment decisions for the same reasons, considering only expected return and standard deviation.
- Every investor has the same market expectations, which allows for the identification of the optimal portfolio.
The market portfolio is key to modern portfolio theory, its existence creating a new strategy for maximizing portfolio return. As a refresher, Karabon records some thoughts about the market portfolio:
- The risk of the market portfolio is measured in both standard deviation and systematic risk.
- No portfolio along the Markowitz efficient frontier has a higher Sharpe ratio than the market portfolio.
- The CML and the Markowitz efficient frontier intercept at the market portfolio.
- The market portfolio is uninvestable.
Marsh & Sons has provided Karabon with data sheets on a number of companies. The first one the analyst considers is Ofin Finance, a consumer-lending company. The sheet contains the following data: expected returns for the stock, the market risk premium, beta, and the risk-free rate of return. Karabon attempts to graph the SML to determine whether the stock is cheaply priced.
The analyst follows up his analysis of Ofin with a review of a half-dozen other stocks. While the SML is a useful tool for assessing valuation, Karabon is not satisfied. He decides to tweak his valuation model by relaxing some of the assumptions used to calculate the SML.
First, Karabon assumes that investors cannot borrow or lend at the risk-free rate. Eliminating the assumption changes the look of the SML graph. Next, Karabon goes down the list of assumptions and determines that every time he relaxes one of the CAPM assumptions, the SML changes dramatically.
When Karabon relaxed one of the CAPM assumptions, the SML looked different depending on the size of the stock. He was relaxing the assumption of:
Relaxing the assumption of no transaction costs and taxes turns the SML into a band, not a line. But since smaller stocks may have a higher liquidity premium than larger stocks, the band may be wider for the smaller stocks. The efficient-market hypothesis is not relevant here.
Which of Karabon’s assumptions about the capital market theory is least accurate?
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A) |
All investors make investment decisions for the same reasons, considering only expected return and standard deviation. | |
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B) |
Every investor has the same time horizon. | |
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C) |
Investors can borrow at the risk-free rate and know in advance about their real cash flows. | |
While investors who theoretically borrow at the risk-free rate would certainly know their nominal cash flows, real cash flows cannot be guaranteed. A number of events, such as a change in the inflation rate, could affect real cash flows.
The risk-free asset is least likely to be/have:
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A) |
needed to calculate the CML. | |
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B) |
needed to calculate beta. | |
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C) |
the point at which the SML intercepts the y-axis. | |
The SML intercepts the y-axis at a point equal to the risk-free rate of return, and that asset is needed to change the efficient frontier from a curve into a line, the CML. However, beta is calculated using the standard deviation, covariances, and correlations.
To calculate the SML for Ofin Finance, Karabon needs:
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A) |
the covariance between the returns for Ofin Finance and the market portfolio. | |
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B) |
expected market returns. | |
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C) |
no data beyond what he already possesses. | |
To calculate the SML for an asset, we need expected returns of that asset and the market, the asset’s beta, the risk-free return, and the market risk premium. However, since the market risk premium equals the expected market return minus the risk-free rate, we can calculate any one of the three variables if we are given the other two. By using the market risk premium and the risk-free rate, Karabon can calculate the expected market return.
Which of Karabon’s statements about the market portfolio is least accurate?
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A) |
The risk of the market portfolio is measured in both standard deviation and systematic risk. | |
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B) |
No portfolio along the Markowitz efficient frontier has a higher Sharpe ratio than the market portfolio. | |
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C) |
The market portfolio is uninvestable. | |
The market portfolio’s risk is generally measured by standard deviation. Systematic risk is used to calculate the SML. Both of the other statements are correct.
How does eliminating the ability to lend and borrow at the risk-free rate change the nature of the SML?
In order to make the SML equation work, a zero-beta portfolio must exist. If we cannot borrow or lend at the risk-free rate, the zero-beta portfolio has a higher expected return than the risk-free rate, which makes the y-intercept higher. The higher return for the zero-beta portfolio also lowers, or flattens, the slope. | 
发表于 2010-4-21 14:41
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