Assignment Investment Theory

Part I

We know from Zou (2006) that the βB=E(x_i x_m )/E(x_m^2 ) =(Cov(x_i,x_m )+E(x_i )E(x_m ))/(Var(x_m )+[E(x_m )]^2 ) and that E(xi)= βB * E(xm)

As in this case we take a long position in asset i, and a short position in asset j, we know that E(xij)=E(xi)-E(xj). Note the minus sign because a positive return on asset j will yield us with a loss.

One can immediately see that this does not hold, because the BCAPM predicts the excess return of an asset in relationship with the excess return of the market.

If we substitute for xi xij in the above formulas, we will see that the equality is invalid, as this equation misses some terms.

Substitution of xi for xij in the above formula, and then for x¬¬ij=(x¬i-xj) will yield this, hence this answer is correct.

If answer a and b are incorrect it is evident that this answer is invalid.

If answer c is correct it is evident that this answer is invalid.

Hence we choose answer c.

By definition we know that E(δx_i )=0

ri denotes gross return not excess, hence this does not hold

holds by definition

Not similar as the market return.

You can’t just sum them up.

As a/d not correct, e does not hold

Hence we choose answer b. (Not too sure about this one)

3.

True, SDF is consistent with no arbitrage and complete market, see slides 5-8 week 1

True, this is essentially the definition of SDF

This one is wrong, as the others are right

True see slide 11 week 1

True see slide