For Q$8-$Q$10,$ consider a market neutral hedge funds invested in the "Betting Against Beta" strategy. The following assets can be

traded.

The hedge funds estimate the following excess returns of the low $-$ and high$-$ portfolios:

$r_t^{\text{l}\text{o}\text{w}}={}^{\text{l}\text{o}\text{w}}+0\mathrm{.}5r_t^{\text{m}\text{a}\text{r}\text{k}\text{e}\text{t}}+{}_t^{\text{l}\text{o}\text{w}}$

$r_t^{\text{h}\text{i}\text{g}\text{h}}={}^{\text{h}\text{i}\text{g}\text{h}}+1\mathrm{.}5r_t^{\text{m}\text{a}\text{r}\text{k}\text{e}\text{t}}+{}_t^{\text{h}\text{i}\text{g}\text{h}}$

where all $r_t\text{'}$s are excess returns, and the error terms ${}_t^{\text{l}\text{o}\text{w}}$ and ${}_t$ high $$ are independent over time and of each other, have zero means

$E({}_t^{\text{l}\text{o}\text{w}})=E({}_t^{\text{h}\text{i}\text{g}\text{h}})=0,$ and annual volatilities of Vvar$({}_t^{\text{l}\text{o}\text{w}})=\sqrt[\phantom{2}]{l}ar({}_t^{\text{h}\text{i}\text{g}\text{h}})=4\%.$

The expected returns of stock portfolios and the risk$-$free asset are given above. NB; expected excess return $=$ expected return $-$ risk$-$

free rate

Hedge fund BBB targets a volatility of $10\%($no target on gross leverage$).$ What is the expected excess return $($i$.$e$.,$ above the risk$-$free

return$)?$ Assume the following for the portfolio weights: $w_{rf}=0,w_{\text{l}\text{o}\text{w}}>0,w_{\text{m}\text{a}\text{r}\text{k}\text{e}\text{t}}=0,$ and Also, assume $-w_{\text{l}\text{o}\text{w}}=3^{*}{w}_{\text{h}\text{i}\text{g}\text{h}}$

a$.3\mathrm{.}75\%$

b$.4\mathrm{.}74\%$

c$.2\mathrm{.}37\%$

d$.4\mathrm{.}24\%$

e$.3\mathrm{.}24\%$

f$.7\mathrm{.}50\%$

Clear my choice