Answer:
Part a)
Arbitrage pricing theory APT pricing theory was basically developed to overcome the limitations of CAPM,CAPM only considers the market risk in order to price any asset however there no. Of risk involved with an asset like liquidity risk, operating risk, interest rate risk, credit risk,economy risk, industry risk,GDP etc.While APT says that the return of any asset for the purpose of pricing has a linear relationship with N no. Of factors which represent different types of risk stated above APT equation is given by
Er= Rf+ B1× F1+B2×F2+B3×F3+.............Bn×Fn + e
Where,
Er= return expected from an asset
Bi= sensitivity of an asset with different factors
Fi= factors
e= asset specific risk
Although APT has two fundamental assumptions
1) there should be a perfectly competitive market
2) no. Of factors should not be more than the no. Assets in the market.
Now as we can see that in this question we are only given Er and Beta i.e. one sensitivity and that too risk factor associated with this beta is also not given hence this data is inconsistent with APT
Part b)
If we want to create a risk risk free portfolio with risky assets only (i.e. no borrowing or investing at Risk free rate) then we need to solve the following two equations
Rf= Erp×Wp+ Erq× Wq
0= Wp+ Wq
First equation says that porfotlio should provide risk less profit
Second equation says that net investment should be Zero
We have
4= 12×Wp+ 15×Wq
0=Wp+Wq
Solving for Wp we get Wp= 4/(-3)= -1.33333
And Wq= 1.3333333
Which means that we should shortsell asset P with133% and buy asset with 133% weight this way we will achieve both of our goal.
Thakyou!
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