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本文主要从definition of the Security Market line分析，由英国作业之英语论文代写策划组提供。

论文题目：assignment
论文语言：英语论文 English
论文专业：金融
字数：500
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论文用于：BA assignment 本科课程作业

1. (a) According to the definition of the Security Market line (SML), the expression of it is shown as:
E[ri] = rf +βi (E[rM] - rf )   (*)
so withβi =σiM / σM2,
σiM =ρiM×σi×σM=0.7×0.2×0.16=0.0224
σM2=(0.16)2=0.0256,
    βi =σiM / σM2=0.0224/0.0256=0.875
bring thisβi to (*), and with rf=0.05, E[rM]=0.1, we can obtain
    E[ri] = rf +βi ( E[rM] - rf )=0.05+0.875×(0.1-0.05)
        =0.09375
As the actually expected return of stock A is 0.11, but the fair return (as predicted by CAPM) is 0.09375, with 0.11>0.09375, so stock A is underpriced.
Firstly, consider another asset A’ which has the same risk as β represents, and it falls on the SML, so with the same risk stock A has a higher return than A’, investors are more favor to buy A and sell A’, consequently, the price of A rises and that of A’ falls down until the market build a new equilibrium. In other words, stock A which falls above SML is underpriced.

 (b) E[r]
                               SML
                 
    0.11           A                  
E[rM]=0.1             M

\

0.875βM =1                  β

     Stock’s alpha is the difference between the actually expected and fair rates of return on a stock, so
 α= actually expected return-fair return
       =0.11-0.09375=0.01625

  (c) Yes, there actually exists such kind of risky stock.
From the equation E[ri] = rf +βi ( E[rM] - rf ) (*), we can obtain that if E[ri]<rf, which means even if the “risk” as measured by σi is very large, βi here is negative. The asset with https://www.51lunwen.org/ukthesis/2012/0611/2331022454.html negative β illustrates the return of this asset moves reverse to the Market Portfolio, and investing in such asset improves the variance of the portfolio, reduces fluctuation of the portfolio and provides insurance of portfolio. Of course, we should be prepared to pay for it, and accept a low rate of return, because adding in such asset could raise the utility of the portfolio. For example, cheap airline company always operates well in depression, so its stock always moves reverse to the Market Portfolio.

2. (a) From the APT equation rp*= β1pλ1+β2pλ2,
     Where rp*= E[rp]-rf, λ1=E[r1]-rf, λ2=E[r2]-rf; and λ represents a risk premium of a portfolio. Then,
     8.0%-6.0%=1.0×λ1+0.6×λ2;
10.0%-6.0%=0.5×λ1+1.8×λ2.
     Form the above two equations, we can conclude λ1=0.008, λ2=0.02, so the risk premia of two factors are 0.8% and 2.0%.

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