The lower panel of Table 1 below lists betas of UST zeroes with respect to the Level and Slope factors based on sample period 1976 to 2018.

a) Consider a portfolio with equal present value weights in each zero. Say $10 in each zero, for a total portfolio value of $100.

What is the portfolio dollar beta on the Level factor?

What is the portfolio dollar beta on the Slope factor?

b) Suppose you tried to hedge the Level risk of a short position in this portfolio with a long position in the 5-year zero.

What present value of the 5-year zero would you need to buy to hedge the Level risk of your net position?

If you bought this amount of the 5-year zero, what would be the dollar beta of your net position on the Slope factor?

Table 1: PCA of UST zeroes 1976-2018
	1 (Level)	2 (Slope)
Factor var. ():	567	14
As % of total:	96.8%	2.4%
Factor vol.:	23.81	3.74
Factor SR:	0.40	0.30
1-year zero q:	0.05	0.19
2-year zero q:	0.11	0.33
3-year zero q:	0.16	0.39
4-year zero q:	0.22	0.41
5-year zero q:	0.28	0.37
6-year zero q:	0.33	0.24
7-year zero q:	0.37	0.07
8-year zero q:	0.41	-0.09
9-year zero q:	0.44	-0.29
10-year zero q:	0.47	-0.50