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I am asked to solve the following homework question: Risk free rate: 2% Expected excess return on market portfolio: 8% Standard deviation of market portfolio: 20% The efficient portfolio has the following: Expected return: 12% Standard deviation: 25%

I am asked the following question: "How can the expected return of the wining portfolio be achieved? Specify the amount invested in each asset/portfolio of assets?" and I've used the following calculation to determine portfolio weight of 1.25: 0.12=ω0.1+(1-ω)0.02⇒ω=1.25

And here is where I am a little lost. What does it mean to have the portfolio weight >1 and what does it mean? If it's incorrect, where did I go wrong before? Thanks for any help!

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  • $\begingroup$ It means that you short the other asset. In this case, it is the risk-free asset you short, which means you are borrowing money. However, how do you get 0.1 in your formula for the market? $\endgroup$ – Raskolnikov Nov 23 '17 at 8:46
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    $\begingroup$ Expected excess return on market portfolio: RM-Rf=0.08 so RM=0.1 $\endgroup$ – turtle101 Nov 23 '17 at 8:57
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    $\begingroup$ So does this mean I invest everything in the risky asset and then borrow 25% more at the risk-free rate? $\endgroup$ – turtle101 Nov 23 '17 at 9:03
  • $\begingroup$ Yeah, but you also invest those borrowed 25% in the market. $\endgroup$ – Raskolnikov Nov 23 '17 at 9:13
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Just to make this a regular reply:

A negative value for a weight means that you short that asset. Inevitably, it also means that the money you get from shorting gets invested into the other assets. Hence weights larger than 1. In your case, it is the risk-free asset you short, which means you are borrowing money. To be precise you borrow 25% at the risk-free rate and invest 125% into the risky assets.

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