3.1.考虑一个具有五种预期收益的风险资产的市场
µ1 = 8%,µ2 = 6%,µ3 = 12%,µ4 = 14%,µ5 = 10%。

imum Variance Portfolio wmin 和 Market Portfolio m 有权重

σwmin =0.2，σm =0.3。
(a) (10 分) 在 Excel 中，绘制最小方差线（这是一条线

(b) (20 分) 根据以上初始数据，推导出公式

(c) 假设我们将 W = 30 000 投资于风险资产，并且

(i)（10分）如果我们愿意，我们应该如何分配投资W

(ii)（10分）如果我们愿意，我们应该如何分配投资W

(d) (10 分) 计算风险资产的 Beta 并给出

Portfolio Theory and Risk Management
Coursework Assignment 3
3.1. Consider a market with ﬁve risky asset with expected returns
µ1 = 8%,µ2 = 6%,µ3 = 12%,µ4 = 14%,µ5 = 10%.
Assume that there exists a risk free asset with return r and that the Min-
imum Variance Portfolio wmin and the Market Portfolio m have weights

Assume that the standard deviations of returns for these portfolios are
σwmin =0.2, σm =0.3.
(a) (10 points) In Excel, plot the Minimum Variance Line (this is a line
of all portfolios with smallest standard deviations for given expected
returns).
(b) (20 points) Based on the above initial data, derive the formula for
the risk free rate r. Compute r in Excel. Plot the Capital Market
Line.
(c) Assume that we invest W = 30 000 into the risky assets and the
risk free asset. Assume that short positions are allowed for the risky
assets, but not for the risk free asset (in other words that we cannot
borrow money risk free).
(i) (10 points) How should we divide the investment W if we wish
to make an optimal investment with standard deviation of the
return equal to 0.2.
(ii) (10 points) How should we divide the investment W if we wish
to make an optimal investment with expected return 10%.
(d) (10 points) Compute Betas of the risky assets and give the plot of
the Security Market Line.