Problem $2$: Evaluating ETFs for HML risk management In this problem we will be managing HLM risk using the following ETFs VUG$-$Rf VTV$-$Rf VTV$-$VUG a $0\mathrm{.}02-0\mathrm{.}03$ b $1\mathrm{.}070\mathrm{.}96$ s $-0\mathrm{.}10-0\mathrm{.}22$ h $-0\mathrm{.}290\mathrm{.}30$ a$)$ Calculate implied factor loadings for the VTV$-$VUG strategy b$)$ Let$$s use this strategy for HML risk management. Assume you have a $$100,000$ position with zero HML loading. Assume you want to increase the HML factor loading by $1$ what trading strategy you would use in terms of HML and in terms of VTV$-$VUG? Strategy in terms of HML$\_\_\_\_\_\_$ Strategy in terms of VTV$-$VUG$\_\_\_\_\_\_\_\_\_$ c$)$ Using the current prices of VTV and VUG from Yahoo finance to calculate the number of shares you need to short$/$long to implement your trading strategy. Total $ traded for VTV$,$ VUG $\_\_\_\_\_\_$ VUG Price$\_\_\_\_\_$ Nshares$\_\_\_\_\_$ SHORT$/$LONG VTV Price$\_\_\_\_\_$ Nshares$\_\_\_\_\_$ SHORT$/$LONG d$)$ Assume HML goes up by $1\%.$ Calculate the change in your VUG$/$VTV position. Namely, report below $\_\_\_\_\_\_$ new price of VUG $\_\_\_\_\_\_$ new price of VTV LOSS$/$GAIN per share of VUG$\_\_\_\_\_\_$ LOSS$/$GAIN per share of VTV$\_\_\_\_\_\_$ Change in total VUG position $\_\_\_\_\_\_$ Change in total VTV position$\_\_\_\_\_\_$ Total change in your position related to VUG$/$VTV $\_\_\_\_\_\_\_\_\_$ Problem $2$: Evaluating ETFs for HML risk management

In this problem we will be managing HLM risk using the following ETFs

a$)$ Calculate implied factor loadings for the VTV$-$VUG strategy

b$)$ Let's use this strategy for HML risk management. Assume you have a $\backslash (\backslash$$ $100,000\backslash )$ position with zero HML loading. Assume you want to increase the HML factor loading by $1$ what trading strategy you would use in terms of HML and in terms of VTV$-$VUG?

Strategy in terms of HML

Strategy in terms of VTV$-$VU

c$)$ Using the current prices of VTV and VUG from Yahoo finance to calculate the number of shares you need to short$/$long to implement your trading strategy.

Total $\backslash$$ traded for VTV$,$ VUG

VUG

Price

Nshares

SHORT$/$LONG

VTV

Price

Nshares

SHORT$/$LONG

d$)$ Assume HML goes up by $1\backslash \%.$ Calculate the change in your VUG$/$VTV position. Namely, report below

new price of VUG

new price of VTV

LOSS$/$GAIN per share of VUG

LOSS$/$GAIN per share of VTV$.$

Change in total VUG position

Change in total VTV position.

Total change in your position related to VUG$/$VTV