Question

12. Portfolio has beta=-0.5; its alpha is -2%, risk free rate is 5%; market expected return is 8%. Find market risk premium R_mt, expected return r_portfolio and excess return R_portfolio. Use formula R_portfolio =beta portfolio *R_market]+alpha+e_portfolio; Where for each security, R=r-r_free is excess return; Is such portfolio over-, under- or fairly priced? Assume, portfolio is well diversified. Which term (s) should be negligible? Follow the guideline below to take the steps using a well- diversified portfolio to build an arbitrage portfolio: Portfolio Weight In Asset Contribution to Excess Return Portfolio P Wplap + Bp Ry+ep) = ap + Bp R+ Op Wp = 1 WuRy - - BPRM Benchmark WM-BP Wy .00 Risk-free asset W, = Bp - 1 w = 0 Portfolio A Op + ep

Answer 1

Beta = -0.5 ; Alpha = -2% ; risk free rate = 5% market expected return 8%.

Market risk Premium :

The amount by which excess market return exceeds risk free rate.

Market Risk Premium (MRP) = rm  - rf

$\therefore$ MRP = 8% - 5% = 3%

It is the reward that investor demand for holding a portfolio with a beta.

MRP is a part of CAPM.

ri = rf + (rm - rf) * $\beta$

ri= 0.05 + (0.08 - 0.05) * -0.5

= -0.04

(i.e) 0.04

Expected Return ( CAPM): Capital Asset Pricing Model:

r = Rf + beta (Rm - Rf) + alpha

Therefore,

$\alpha$ = R - Rf - $\beta$ (Rm - Rf)

here, Rf + beta (Rm - Rf) + alpha

r = 0.05 + (-0.5) (0.08-0.05) + (-0.02)

r= 0.05 + (-0.015) + (-0.02)

r = 0.015 or 1.5%

The excess return of an investment which relates to the Return of a benchmark index .

Alpha can be used as a metric for evaluating performance of a manager overall.

In investment , there is also a metric known as jensen's Alpha:

Here, Jenson Alpha is calcualted as:

Jensen's Alpha = R(i) -(R(f) +B(R(m)- R (f)))

Conclusion:

CAPM predicts that alpha should be Zero for all the Assets.

The alpha of the stock is its expected return in excess of the fair expected return .

If the stock is fairly priced ,its alpha must be Zero.