This is from the 2014 June mock PM, set 9, question 4: if Donner wants to construct an optimal portfolio with an expected S.D of 12%, he should combine his proposed fully diversified portfolio with which of the following: borrow 20% assets; lend 20% assets; lend 80% assets?

The fully diversified portfolio has expected return =13% and S.D=15%, risk free=4% Can someone please explain how they got lend 20% of assets?

His tangent portfolio has a higher std dev than what is prefered, so he has to reduce his risk. He does so by buying Rf securities, essentially lending at the risk free rate.

The 20% is arbitrary -> no calculation is needed given our available answers

Just figure out the portfolio weights. You know the stdev of Rf is zero and target is 12% so you must have 80% in the risky asset and 20 in the risk free asset.

and that’s how you can get the weight of Risky assets (which is 80%), so in order to “complete” the investment, you lend (invest) 20% of the assets in the RFR

The 20% is not remotely arbitrary. His portfolio has σ = 15% and he wants σ = 12% = 80% × 15%. So he wants 80% of his portfolio and 20% (= 100% – 80%) of the risk-free asset.