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卢天悦 · 2023年07月29日

这题一定要分开算吗,可以把两个目标合在一起直接算不

NO.PZ2022123002000055

问题如下:

Ari Patheo, a portfolio manager for Astute Investments, manages a 280 million U.S. dollar (USD) investment portfolio. Astute’s investment committee has recently become more risk averse in anticipation of a major announcement regarding monetary policy. To reflect this view, Patheo wishes to temporarily make the following changes in the portfolio:

Ÿ decrease the portfolio’s equity allocation and decrease its equity beta;

Ÿ increase the portfolio’s bond allocation and decrease its modified duration.

The portfolio’s current and target characteristics are shown in Exhibit 1.

Exhibit 1 Investment Portfolio Characteristics

Patheo does not want to incur high trading costs for a temporary reallocation and decides to use the following futures contracts to achieve the portfolio targets.

Ÿ equity futures - currently priced at USD 129,000 per contract (after accounting for the multiplier), with an equity beta of 0.97;

Ÿ bond futures - currently priced at USD 103,000 per contract, with a modified duration of 7.70 and a yield beta of 1.00.

Determine the action (buy or sell) and the number of futures contracts required to achieve the:

i. equity targets.

ii. bond targets.

Show your calculations.

选项:

解释:

Correct Answer:

i. Equity targets

Patheo effectively needs to sell $28 million of stock by converting it to cash using stock index futures and buy $28 million of bonds by using bond futures. This would effectively convert the stock into cash and then convert that cash into bonds. Of course, this entire series of transactions will be synthetic; the actual stock and bonds in the portfolio will stay in place.

In order to achieve the equity targets, Patheo must determine the number of equity futures necessary to:

1. Reduce the equity allocation by $28 million and

2. Decrease the equity beta to 0.90

In both cases Patheo will rely on the following relationship: Nfe = [(βT – βP) / (βf)] × (E / fe)

To Reduce the Equity Allocation by $28 million:

Patheo wants to reduce equities by USD 28,000,000, so the target beta is the beta of cash, which is assumed to be zero. The portfolio’s current beta is 1.08 and the futures’ beta is 0.97.

Therefore, Nfe = [(0 – 1.08) / (0.97)] × (28,000,000 / 129,000) = –241.67.

Patheo should sell 242 equity futures contracts.

To Decrease the Equity Beta to 0.90:

Next, Patheo needs to decrease the equity beta from 1.08 to 0.90 on what is now a USD 154,000,000 equity portfolio.

Therefore Nfe = [(0.90 – 1.08) / (0.97)] × (154,000,000 / 129,000) = –221.53

Patheo should sell 222 equity futures contracts.

To achieve the equity targets, Patheo should sell 242 + 222 = 464 equity futures contracts.

ii. Bond targets

In order to achieve the bond targets, Patheo must determine the number of bond futures necessary to:

1. Increase the bond allocation by $28 million and

2. Decrease the modified duration to 6.0

In both cases Patheo will rely on the following relationship:

Nfb = [(MDURT – MDURP) / MDURf] × (B/fb)

To Increase the Bond Allocation by $28 Million:

Patheo wants to increase bond exposure by USD 28,000,000. The starting position for this is the synthetic cash which has been raised by the sale of equity futures, so the modified duration of this component is zero.

Therefore Nfb = [(7.20 – 0.00) / 7.70] × (28,000,000 / 103,000) = 254.19

Patheo should buy 254 bond futures contracts.

To Decrease the Modified Duration to 6.0:

Next, Patheo needs to change the modified duration from 7.20 to 6.00 on what is now a USD 126,000,000 bond portfolio.

Nfb = [(6.00 – 7.20) / 7.70] × (126,000,000 / 103,000) = –190.64

Patheo should sell 191 bond futures contracts.

To achieve the bond targets, Patheo should buy 254 – 191 = 63 bond futures contracts.

结果应该是一样的

1 个答案
已采纳答案

pzqa31 · 2023年07月30日

嗨,从没放弃的小努力你好:


个人认为如果考主观题不要合在一起,做计算题的话只要能算对分开还是合在一起都是可以的。

----------------------------------------------
努力的时光都是限量版,加油!

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2024-07-31 19:06 1 · 回答

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2024-07-28 17:04 3 · 回答