m****s
发帖数: 1481 | 1 看到这样一道题：
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Question : An investor has a portfolio with a value of $1,000,000 and a
beta of 2.5. He believes the portfolio carries more market risk than he
desires and wishes to reduce the beta to 1. How many futures contracts
should be buy or sell to reduce the beta if the futures contracts have a
beta of 1.2 and the notional value of each contract is $240,000?
(a) Buy 4 contracts
(b) Sell 5 contracts
(c) Sell 9 contracts
(d) Buy 1 contracts
Your Answer is Correct
The correct answer is choice 'b'
The investor's needs to sell futures contracts, as his current position is
long. He needs to sell ($1,000,000 x (2.5-1)) / ($240,000 x 1.2) = 5.2
contracts, or rounded to 5 contracts.
It is important to note here that the investor wishes to retain a beta of 1,
and does not want to get rid of all market exposure.
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这个答案对吗？我怎么记得portfolio的beta应该是weighted beta之和，那么这个需要
short的contract假设是N的话应该满足
1000000x2.5+Nx240000x1.2=1x(1000000+Nx240000)
算出来N=-31.25? | l**h
发帖数: 7994 | 2 为什么不是下面的公式？
1000000x2.5 =1x1000000+Nx240000x1.2
a | m****s
发帖数: 1481 | 3 不是说portfolio的beta是各个asset的beta的加权之和吗？
beta_p=sum(w_1*beta_1+w_2*beta_2+...)
就这道题而言，难道不应该是
beta_p=1
w_1=1000000/(1000000+240000*N)
w_2=240000*N/(1000000+240000*N)
?
【在 l**h 的大作中提到】
: 为什么不是下面的公式？
: 1000000x2.5 =1x1000000+Nx240000x1.2
: a
| x********9
发帖数: 31 | 4 240,000 is just the notional of future. It does not add up to portfolio
value. | m****s
发帖数: 1481 | 5 谢谢两位解释，可以这样理解么
相当于future的涨跌对冲了原来的asset的跌涨使得beta减小，但是portfolio本身还是
只有原来的，future的notional因为并没有真正change hand所以对portfolio
notional没影响，是么？ |
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