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

Asset class

Expected annual return

Market $\backslash$beta

Risk free

$2\%$

$0$

Portfolio of low $\backslash$beta stocks

$6\%$

$0\mathrm{.}5$

Market portfolio

$7\%$

$1\mathrm{.}0$

Portfolio of high $\backslash$beta stocks

$8\%$

$1\mathrm{.}5$

Let wrf$,$ wlow, wmarket, and whigh denote the portfolio weights of the investment in each of the asset classes such that wrf $+$ wlow $+$ wmarket $+$ whigh $=1.$ According to its investment mandate, hedge fund AAA should target a gross leverage of $2.$ Which portfolio will this hedge fund hold?

NB: gross leverage is the sum of the absolute value of portfolio weights.

Question $8$Answer

a$.$

wrf $=-1,$ wlow $=1\mathrm{.}5,$ wmarket $=0,$ whigh $=-0\mathrm{.}5$

b$.$

wrf $=0,$ wlow $=1,$ wmarket $=1,$ whigh $=-1$

c$.$

wrf $=-1,$ wlow $=-1,$ wmarket $=0,$ whigh $=3$

d$.$

wrf $=0,$ wlow $=1\mathrm{.}5,$ wmarket $=0,$ whigh $=-0\mathrm{.}5$

e$.$

wrf $=1,$ wlow $=1,$ wmarket $=0,$ whigh $=-1$

f$.$

wrf $=-1,$ wlow $=3,$ wmarket $=0,$ whigh $=-1$