[問題] 求算標準差
大家好，我是管院的學生，但對統計不拿手，有個題目想請教大家:
An investor holding a portfolio consisting of two stock invests 25% of assets
in Stock A and 75% into Stock B. The return RA from Stock A has a mean of 4%
and a standard deviation of σA=8%. Stock B has an expected return E(RB)=8%
with a satandard deviation of σB=12%. The portfolio return is
P = 0.25RA + 0.75RB.
(a) Compute the expected return on the portfolio.
因為已知股票A、B的期望值，所以就帶入方程式
P = 0.25 * 4% + 0.75 * 8% = 7%
(b) Compute the standard deviation of the returns on the portfolio assuming
that the two stocks' returns are perfectly positively correlated.
目前已知A股票期望值4%，標準差8%；B股票期望值8%，標準差12%
要求整體報酬的標準差，並假設A、B股票完全正相關
var(0.25RA + 0.75RB)
= 0.0625 * var(RA) + 0.5625 * var(RB) + 2 * 0.25 * 0.75 * cov(RA,RB)
= 0.0625 * (0.08)^2 + 0.5625 * (0.12)^2 + 0.375 * cov(RA, RB)
￣￣￣￣ ￣￣￣￣ ￣￣￣￣￣￣
直接用標準差平方得到變異數，不知道對不對?
另外，共變數也不知道該如何求得?
請問這題該如何下手呢? 本來想說求得共變數後再開根號，應該就可以得到
題目要的標準差，但好像被我弄得更複雜了...
(c) Compute the standard deviation of the returns on the portfolio assuming
that the two stocks' returns have a correlation of 0.5.
如果仿造前一小題，共變數用0.5帶入不知道是否正確，因為答案是負值?
var(0.25RA + 0.75RB)
= 0.0625 * var(RA) + 0.5625 * var(RB) + 2 * 0.25 * 0.75 * cov(RA,RB)
￣￣￣￣￣
= 0.0625 * (0.08)^2 + 0.5625 * (0.12)^2 + 0.375 * 0.5
￣￣￣
= 0.0004 + 0.0081 + 0.1875
= 0.196
→ σ=0.4427
(d) Compute the standard deviation of the returns on the portfolio assuming
that the two stocks' returns are uncorrelated.
依然仿造前一小題，彼此無關，表示彼此獨立，則共變數為0
var(0.25RA + 0.75RB)
= 0.0625 * var(RA) + 0.5625 * var(RB) + 2 * 0.25 * 0.75 * cov(RA,RB)
￣￣￣￣￣
= 0.0625 * (0.08)^2 + 0.5625 * (0.12)^2 + 0.375 * 0
￣￣
= 0.0004 + 0.0081 + 0
= 0.0085
→ σ=0.0922
以上幾題是套課本所給的公式，但我不知道是否正確
所以錢來這裡詢問大家，希望大家協助解惑，謝謝~~
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09/23 13:07, , 1F
09/23 13:07, 1F
抱歉，我看錯了，已更正
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09/23 13:08, , 2F
09/23 13:08, 2F
請問完全正相關的corr(RA,RB)是多少阿? 因為RA,RB的標準差都已經已知
※ 編輯: takumix 來自: 112.104.10.208 (09/23 13:37)
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