FRM5 - Modern Portfolio Theory and Capital Asset Pricing Model

Question 1

Explain Modern Portfolio Theory and interpret the Markowitz efficient frontier

Answer 1

MPT asserts how investors should construct portfolios based on certain assumptions about investor behaviour and the properties of capital markets

Efficient frontier is found by plotting the optimal returns for each level of risk

Question 2

Understand the derivation and components of the CAPM

Answer 2

E(Ri) = r + Bi (E(Rm) - r)

Where E(Ri) is expected rate of return of asset i, r is rate of return in risk free asset, market risk premium is E(Rm) - r and Bi is quantity of market rate

Question 3

Describe the assumptions underlying the CAPM

Answer 3

• information to market information of all participants is easily available and instantly absorbed by participants
• all market participants have the same expectations
• all market participants make decisions based off of mean and variance of returns
• no transaction costs or taxes
• allocations can be made in an investment of any partial amount
• all participants borrow and lend at common risk free interest rate
• individual investors allocation decision can not change market prices

Question 4

Interpret and compare the capital market line and the security market line

Answer 4

Capital market line is all portfolios that can be made when a risk free asset is introduced, dominates all portfolios except tangency portfolio

Security market line shows the relationship between expected return for individual assets and risk, proxied by beta rather than standard deviation

Question 5

Apply the CAPM in calculating the expected return on an asset

Answer 5

E(Ri) = r + Bi (E(Rm) - r)

Question 6

Interpret beat and calculate the beta of a single asset or portfolio

Answer 6

Beta estimated by R_it - r_t + a_i + b_i(R_mt - r_t+ error_t

Betas compare risk compared to the market, high beta means higher risk than the market

Question 7

Calculate, compare, and interpret the following performance measures: the Sharpe performance index, the Treynor performance index, the Jensen performance index, the tracking error, information ratio, and Sortino ratio

Answer 7

Sharpe = (E(R_i) - r) / sigma_i, greater than slope of capital market line indicates superior performance than expected in equilibrium

Treynor = (E(R_i) - r) / beta_i, greater than E(Rm) - r means superior performance

Jensen: Rbar_i - r = alphahat_i + betahat_i(Rbar_m - r), if a significantly different to zero positive shows indicates superior performance

Sortino = (R_p - T) / sqrt( 1/N * sum(t = 1 to N) min(0, R_pt -T)^2 ) where T is the target rate of return for an investment strategy

Tracking error = Rp - Rb where Rb is return on client specified portfolio

Information ratio = average active return / tracking error