paul Yang 發問時間： 社會與文化語言 · 1 0 年前

# risk and return 請大德們能幫忙解惑(20點)

Precival Hygiene has \$10 million invested in long-term corporate bonds. This bond portfolio’s expected annual rate of return is 9 percent, and the annual standard deviation is 10 percent

Amanda Reckonwith, Percival’s financial adviser, recommends that Percival consider investing in an index fund which closely tracks the Standard and Poor’s500index. The index has an expected return of 14 percent, and its standard deviation is 16 percent.

A.Suppose Percival puts all his money in a combination of the index fund and Treasury bills. Can he there by improve his expected rate of return without changing the risk of his portfolio? The Treasury bill yield is 6 percent.

B. Could Percival do even better by investing equal amounts in the corporate bond portfolio and the index fund? The correlation bond portfolio and the index fund? The correlation between the bond portfolio and the index fund is +.1.

### 3 個解答

• 書揚
Lv 5
1 0 年前
最佳解答

Precival Hygiene has \$10 million invested in long-term corporate bonds. This bond portfolio’s expected annual rate of return is 9 percent, and the annual standard deviation is 10 percent

Precival Hygiene投資了一千萬美元在長期公司債券上。此債券投資組合的預期報酬率每年是9%，並且標準差為10%。

Amanda Reckonwith, Percival’s financial adviser, recommends that Percival consider investing in an index fund which closely tracks the Standard and Poor’s500index. The index has an expected return of 14 percent, and its standard deviation is 16 percent.

Amanda Reckonwith，是Percival 的財政顧問，她建議 Percival 考慮投資指數基金，此基金緊隨著標準普爾500指數。這指數基金預期會有14%的報酬率， 標準差為16%。

A. Suppose Percival puts all his money in a combination of the index fund and Treasury bills. Can he there by improve his expected rate of return without changing the risk of his portfolio? The Treasury bill yield is 6 percent.

A. 假設Percival 投入他所有的錢在指數基金和國庫券。他可以在不改變投資組合的風險下而增加他的預期報酬率嗎？國庫券的收益率是6%。

B. Could Percival do even better by investing equal amounts in the corporate bond portfolio and the index fund? The correlation bond portfolio and the index fund? (這句是不是重複下面那一句？或打錯了？)The correlation between the bond portfolio and the index fund is +.1.

B. 若Percival 投資等額資金在公司債券和指數基金上，他能賺到更多的報酬率嗎？ 債券投資組合和指數基金相關係數為+0.1。

PS：你是要翻譯，還是要答案？

2008-04-28 22:19:46 補充：

投資組合的預期報酬率及標準差公式如下：

E(Rp)=W1*R1+W2*R2 ----> W1 +W2=1

σp^2=W1^2*σ1^2+ W2^2*σ2^2+2* W1*W2*σ12

σ12=ρ12*σ1*σ2 ----> ρ12為相關係數

2008-04-28 22:20:40 補充：

A. ：若要不改變投資組合的風險，則這個由指數基金和國庫券所組成的投資組合的標準差應不高於(亦即小於等於)原先債券投資組合的10%。

通常我們都視國庫券為無風險證券，所以其標準差為0。

將這些數據代入下式，

σp^2=W1^2*σ1^2+ W2^2*σ2^2+2* W1*W2*σ12= W1^2*σ1^2

所以σp=W1*σ1

10%= W1*16%

W1=5/8

E(Rp)=W1*14%+(1-W1)*6%=5/8*14%+3/8*6%=11%

因此若將資金的5/8(亦即625萬美元)在指數基金，而3/8(375萬美元)在國庫券上，其風險沒有增加，但報酬率卻由9%上升到11%。

2008-04-28 22:21:03 補充：

B. ：E(Rp)=1/2*9%+1/2*14%=11.5%

σp^2=(1/2)^2*(10%)^2+ (1/2)^2*(16%)^2+2* (1/2)*(1/2)*0.1*(10%)*(16%)

σp=9.85%

可以，若投資等額資金在公司債券和指數基金上，此時投資報酬率為11.5%，但標準差卻只有9.85%而己，這表示這個投資組合的風險降低，但報酬卻增加了。

參考資料： 自己
• Joana
Lv 5
1 0 年前

Precival Hygiene has \$10 million invested in long-term corporate bonds. This bond portfolio’s expected annual rate of return is 9 percent, and the annual standard deviation is 10 percent

Precival Hygiene投資了一千萬美元在長期公債。證券單預期每年的回報率是百分之9, 並且每年標準偏差是百分之10

Amanda Reckonwith, Percival’s financial adviser, recommends that Percival consider investing in an index fund which closely tracks the Standard and Poor’s500index. The index has an expected return of 14 percent, and its standard deviation is 16 percent.

Amanda Reckonwith, 是Percival 的財政顧問, 她建議 Percival 考慮(改成)投資緊跟著the Standard and Poor's500index 的指數基金。這指數基金預料有百分之14的報酬率, 並且它的標準偏差是百分之16 。

A. Suppose Percival puts all his money in a combination of the index fund and Treasury bills. Can he there by improve his expected rate of return without changing the risk of his portfolio? The Treasury bill yield is 6 percent.

A. 假設Percival 投入他所有的金錢在指數基金和國庫債券的組合。他可以因此增加他的回收報酬率卻不必承擔更改證券單的風險嗎? 國庫債券收益是百分之6 。

B. Could Percival do even better by investing equal amounts in the corporate bond portfolio and the index fund? The correlation bond portfolio and the index fund? The correlation between the bond portfolio and the index fund is +.1.

Percival 可以投資等額的公司債券和指數基金而賺得更多嗎? 還是交互投資公債和指數基金? 交互投資公債和指數基金的回收報酬率是+.1 。

• 1 0 年前

Precival Hygiene has \$10 million invested in long-term corporate bonds. This bond portfolio’s expected annual rate of return is 9 percent, and the annual standard deviation is 10 percent

Amanda Reckonwith, Percival’s financial adviser, recommends that Percival consider investing in an index fund which closely tracks the Standard and Poor’s500index. The index has an expected return of 14 percent, and its standard deviation is 16 percent.

A.Suppose Percival puts all his money in a combination of the index fund and Treasury bills. Can he there by improve his expected rate of return without changing the risk of his portfolio? The Treasury bill yield is 6 percent.

B. Could Percival do even better by investing equal amounts in the corporate bond portfolio and the index fund? The correlation bond portfolio and the index fund? The correlation between the bond portfolio and the index fund is +.1.

參考資料： 自己