The price on the non-dividend paying stock is calculated using the formula

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The non-dividend paying stock's price is calculated using the formula F = 50(1 + rf).

Where rf denotes the free interest rate (with annual compounding, as stated).

The risk free interest rate is recovered from the CAPM in order to find it, given the lack of knowledge on the nature of the risk. RE = rf + E is the formula for calculating equity and cost of capital (E[rm] – rf ) 0.1 = rf + 1 × 0.06 rf= 0.04 F = 50 × 1.04 = 52

Assuming the debt was risk-free in this perspective is unreasonable and the presumption made was a close to full score. However this assumption iss explicit and would have been estimated as

F = 50 × 1.05 = 52.5

cov(rz, rm) = ρ(rz, rm) · σz · σm

0.45√ 0.0121√ 0.0169 = 0.006435

var(rm) = 0.0121

βz = cov(rz, rm)

var(rm) = 0.006435

0.0169 = 0.53

E[rz] = rf + (E[rm] − rf )βz

0.063 + (0.148 − 0.063) · 0.53 = 10.8%.

Question 7b (Quarter page): Report the ‘current weights’ of your stocks in the market portfolio (ASX200 or S&P500) using a table. One source for the ASX200 weights is . One source for the S&P500 weights is .

In the same table, add another row called ‘adjusted weights’. We want to adjust the weights of your 5 stocks in the market portfolio so that they add to one and can be input into the Black-Litterman (BL) model. Do this by adding all 5 weights together (call it sumOfWeights which will be less than one), then divide each stock’s weight by the sumOfWeight. Now all of the 5 adjusted weights should sum to one. Report your results. For example, say you had companies A, B, C, D and E which had a 0.02 (2%) weight each in the market portfolio. The sumOfWeights of the 5 stocks would be 0.1. So each stock would have an adjusted weight of 0.2 (=0.02/0.1).

Question 7c (Quarter page): Use the Black-Litterman approach to estimate the returns on your stocks based on their (adjusted) weights in the market portfolio. Since you don’t have the covariance matrix of all stocks in the market, just use the covariance matrix of your 5 stocks. Report the stocks’ BL-implied returns in a table together with their adjusted weights in the market portfolio.

The combined return vector equation of the Black Litterman model is;


E[R] = combined return vector (Nx1 matrix)

Ω = uncertainty in the views and is a diagonal covariance matrix of error terms

Tau (τ) = weight on views scalar

Σ = variance-covariance matrix (NxN matrix).

P = matrix of the assets involved in views (KxN matrix)

Π = implied excess equilibrium returns (Nx1 matrix column vector)

Question 7d (Quarter page): Repeat the above, but take a view that one stock (pick any that’s your favorite) will outperform one other (your least favourite) by 1% per month. Report the stocks’ new BL-implied returns in a table together with their revised weights.

A forward price on non-dividend paying stock will be found as F = 50(1 + rf ) where rf is the risk free interest rate (with annual compounding, as stated). Need to find the risk free interest rate. We don’t know the debt is risk free, hence recover the risk free rate from the CAPM and the equity cost of capital

rE = rf + βE(E[rm] − rf ) 0.1 = rf + 1 × 0.06 rf = 0.04 F = 50 × 1.04 = 52

Note though that assuming debt was risk free was a not unreasonable assumption, so people who stated that they made that assumption got close to full score. But this assumption must have been made explicitly. Would then have gotten an estimate of

F = 50 × 1.05 = 52.5

May 10, 2023

Business Life

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Stock Interests Risk

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