The gap between is just the page split all the relevant info

The gap between is just the page split, all the relevant information has been uploaded. Let me know what is unclear!

3. (Bounds on relurns) Consider a universe oi jusi three securitics They havc expeced 1 ates of return o! 10%, 20%, and 10% respectively Two portfolios are known to lie on THlE CAP!TAL ASSET PRICING MODEL fhe mininm-variance se They e defined by lhe portfolio weights 60 1 807 20 40 lt is also known that the market portfolio is eficient (a) Given this nomton, wha are ihe mininum and maximum possible values for the expecied rae o reurn on the markei porifolio? are told b) Now suppose you w represents the minimum-vaiance portfolio Does this change your answers lo pTt (a)?

Solution

It is given that there are 3 securities with returns 10%, 20% and 10% respectively.

Now let us determine the average return of the two portfolios first :

Rw= 10%×0.60 + 20%×0.20 + 10%×0.20 = 12%

,Rv= 10%×0.80 + (-20%)×0.20 + 10%×0.40 = 8%.

Now Expected return of Market portfolio is = a*12%+ (1-a)*8%

Minimum value of this portfolio, when 1-a = 1 or a = 0, this imlies that we should invest everything in v

Minimum value of this portfolio, when 1-a = 0 or a = 1, this imlies that we should invest everything in w

b) If w is the minimum variance portfolio, it means that this is the minimum return which we can earn given the level of risk

in that case, then there is no sense of investing in v, because we can earn 12% with the minimum risk to the portfolio

So our minimum return is now 12% (Not 8% which is in a))