Question

Capital Asset Pricing Model (CAPM) a. What is two-fund portfolio separation and why is it important? b. Show graphically (in return-standard deviation space) how 2-fund separation works in the context of the CAPM. c. Explain and show how risk averse investors are better off with capital markets. d. What are some of the assumptions that need to hold in order for the CAPM to be applied and why are they important? e. Suppose a stock has a covariance with the market of 0.3 and the market has a variance of 0.2. What is the stock's beta? Is the stock more or less risky than the market? f. Explain why it is important to assume that investors already hold the value- weighted “market”, or tangency, portfolio in order to apply the Capital Asset Pricing Model (CAPM). ann

Answer 1

a.Two fund portfolio separation:

A theory stating that under conditions in which all investors borrow and lend at the riskless rate, all investors will either choose to possess a risk-free portfolio or the market portfolio.

Importance

The extension tells us that when the uncertainty model is convex, an investor with quadratic utility and uncertainty aversion can separate her investment problem into two steps: First, find the portfolio of risky assets that maximizes the worst-case SR (over all possible asset return statistics); and then, decide on the mix of this risky portfolio and the risk-free asset, depending on the investor’s attitude toward risk. The risky portfolio is the TP corresponding to the least favorable asset return statistics, with portfolio weights chosen optimally.

c.

A risk averse investor is an investor who prefers lower returns with known risks rather than higher returns with unknown risks. In other words, among various investments giving the same return with different level of risks, this investor always prefers the alternative with least interest.

Description: A risk averse investor avoids risks. S/he stays away from high-risk investments and prefers investments which provide a sure shot return. Such investors like to invest in government bonds, debentures and index funds.

D. Assumptions

The two-step asset allocation process is based on the assumption that there is no model uncertainty or model mis-specification, i.e., the input data or parameters (the mean vector and covariance matrix of asset returns) are perfectly known. These input parameters are typically empirically estimated from historical data of asset returns, or from extensive analysis of various types of information about the assets and macro-economic conditions.

E.
beta = covariance i variance

thus, o.3/0.2 =1.5

Here, the beta is more than 1 which implies that stock swings more than market hence it is more risky.

F.

Modern financial theory rests on two assumptions: (1) securities markets are very competitive and efficient (that is, relevant information about the companies is quickly and universally distributed and absorbed); (2) these markets are dominated by rational, risk-averse investors, who seek to maximize satisfaction from returns on their investments.

The first assumption presumes a financial market populated by highly sophisticated, well-informed buyers and sellers. The second assumption describes investors who care about wealth and prefer more to less. In addition, the hypothetical investors of modern financial theory demand a premium in the form of higher expected returns for the risks they assume.