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CFA KING · 2023年05月17日

how to calculate the number $15

NO.PZ2023040601000033

问题如下:

The bank’s proprietary fixed-income portfolio is structured as a barbell portfolio: About half of the portfolio is invested in zero-coupon Treasuries with maturities in the 3- to 5-year range (Portfolio P1), and the remainder is invested in zero-coupon Treasuries with maturities in the 10- to 15-year range (Portfolio P2). Georges Montes, the portfolio manager, has discretion to allocate between 40% and 60% of the assets to each maturity “bucket” He must remain fully invested at all times. Exhibit 1 shows details of this portfolio.


If Montes is expecting a 50 bp increase in yields at all points along the yield curve, which of the following trades is he most likely to execute to minimize his risk?

选项:

A.

Sell $35 million of P2 and reinvest the proceeds in three-year bonds

B.

Sell $15 million of P2 and reinvest the proceeds in three-year bonds.

C.

Reduce the duration of P2 to 10 years and reduce the duration of P1 to 3 years

解释:

Duration is a measure of interest rate risk. To reduce risk in anticipation of an increase in interest rates, Montes would seek to shorten the portfolio’s duration. He is limited, however, in the amount he can shift from P2 to P1. Selling $15 million of P2 reduces that portfolio to the lower end of the permitted 40% to 60% range. By reinvesting the proceeds at the shortest maturities allowed, Montes substantially reduces the portfolio duration.

how to calculate the number $15

1 个答案

星星_品职助教 · 2023年05月17日

同学你好,

本题预期利率会上涨(a 50 bp increase in yields),这会导致债券价格下跌。所以要尽量减少债券组合的duration以减少亏损。

由于题目要求“remain fully invested at all times”,所以只能只能尽可能卖掉P2(duration高)然后去尽可能多的买P1(duration低)。

题目要求两种债券的投资范围为40%-60%之间( allocate between 40% and 60%),此时两资产之和50.3m+58.7m=109m,所以P1最高可以持有109m*60%=65.4m。

目前P1的持有量为50.3m,所以最多还能买65.4-50.3=15.1m,最多买15.1m。

整个流程就是卖掉15.1m的P2,用这15.1m买入P1( three-year bonds)。即B选项。