Question

it says to answer 3 parts in this question. so A,B and C please

1. Answer three parts of the following question. Your answer for each part should be no longer than two pages long A. Compare and contrast the capital asset and arbitrage pricing theory models. B. Use the single index model to derive an econometric model of the capital asset pricing model. C. A fully diversified portfolio will have no risk. True or false? Explain your answer. D. Graphically illustrate the efficient frontier facing an investor that cannot short sell risky assets under the following two cases (i) when there is a risk-free asset available and (ii) when there is no risk-free asset available. Explain your answer. E How would you perform a test of the predictions of the capital asset pricing model given historical data on asset and market portfolio returns? F. Evaluating portfolio performance using Sharpe, Treynor, and Jensen.

Answer 1

A. Compare and contrast between CAPM and APT-

• The CAPM allows investors to quantify the expected return on an investment given the investment risk, risk-free rate of return, expected market return, and the beta of an asset or portfolio. The APT serves as an alternative to the CAPM, and it uses fewer assumptions and may be harder to implement than the CAPM.
• An asset's or portfolio's beta measures the theoretical volatility in relation to the overall market. Unlike the CAPM, the APT does not indicate the identity or even the number of risk factors.
• The formula used in CAPM is: E(ri) = rf + βi * (E(rM) - rf), where rf is the risk-free rate of return, βi is the asset's or portfolio's beta in relation to a benchmark index, E(rM) is the expected benchmark index's returns over a specified period, and E(ri) is the theoretical appropriate rate that an asset should return given the inputs. The APT formula is E(ri) = rf + βi1 * RP1 + βi2 * RP2 + ... + βkn * RPn, where rf is the risk-free rate of return, β is the sensitivity of the asset or portfolio in relation to the specified factor and RP is the risk premium of the specified factor.
• The arbitrage pricing theory is an alternative to the CAPM that uses fewer assumptions and can be harder to implement than the CAPM.
• While both are useful, many investors prefer to use the CAPM, a one-factor model, over the more complicated APT, which requires users to quantify multiple factors.

B. Deriving an econometric model of CAPM using single index model-

$R_{it}&space;=&space;\alpha_i+\beta_i&space;\cdot&space;R_{mt}&space;+&space;\epsilon_{it}$

• $R_{it}$ is the return of the stock of observation
• $R_{mt}$ is the return of the reference market
• $\beta_i$ is the regression coefficient between the observed stock and the reference market
• $\alpha_i$ is the regression intercept between the observed stock and reference
• $\epsilon_{it}$ is the error (a random variable with expectation zero and finite variance)

The single-index model assumes that once the market return is subtracted out the remaining returns are uncorrelated:

$E((R_{i,t} - \beta_i m_t) (R_{k,t} - \beta_k m_t)) = 0,$

which gives

$Cov(R_i, R_k) = \beta_i\beta_k\sigma^2.$

C. False.

All investments are subject to risk. It is generally believed that investors are rewarded for taking risk. However, some risk is not rewarded. Investors need to control or eliminate risks for which they are not rewarded from their investment portfolio. Investment risks can be placed into two broad categories: unsystematic and systematic risks. Unsystematic risk (also called diversifiable risk) is risk that is specific to a company. This type of risk could include dramatic events such as a strike, a natural disaster such as a fire, or something as simple as slumping sales. Two common sources of unsystematic risk are business risk and financial risk.

Diversification can greatly reduce unsystematic risk from a portfolio. It is unlikely that events such as the ones listed above would happen in every firm at the same time. Therefore, by diversifying, one can reduce their risk. There is no reward for taking on unneeded unsystematic risk.

On the other hand, some events can affect all firms at the same time. Events such as inflation, war, and fluctuating interest rates influence the entire economy, not just a specific firm or industry. Diversification cannot eliminate the risk of facing these events. Therefore, it is considered un-diversifiable risk. This type of risk accounts for most of the risk in a well-diversified portfolio. It is called systematic risk or market risk. However, the expected returns on their investments can reward investors for enduring systematic risks.

In conclusion, it can be said that diversification reduces risk but does not eliminate it completely.