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I’m looking for a nice & detailed explanation for how to derive the formula for the weight of asset 1 in the tangency / maximum Sharpe ratio portfolio in Markowitz portfolio theory in a world with two risky assets and one risk-free investment. I tried but failed to derive myself, hence I’m looking for a reference.

The sources which I found only describe the general approach of how to derive the portfolio with the highest Sharpe ratio and only present the final formula (e.g. slide 42 of this presentation: http://www.kellogg.northwestern.edu/faculty/papanikolaou/htm/FINC460/LN/Lecture1.pdf)

Any recommendations?

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  • $\begingroup$ Your link is not working to me. $\endgroup$
    – simmy
    May 19, 2016 at 9:13
  • $\begingroup$ Sorry, have corrected a type in the link in the meantime $\endgroup$
    – tk79
    May 19, 2016 at 12:35

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in my book Introduction to Mathematical Portfolio Theory, we give two different derivations.

Most books give at least one, eg Luenberger, Pennacchi

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In: MODERN PORTFOLIO THEORY AND INVESTMENT ANALYSIS - ELTON, GRUBER, BROWN, GOETZMANN , chapter 5, you can find a good explanation of your issues.

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  • $\begingroup$ I've checked the 9th edition. Unfortunately it doesn't cover this. $\endgroup$
    – tk79
    May 20, 2016 at 7:05
  • $\begingroup$ Maybe you are right, in chapter 5 (yes nine edition) are shown various case with 2 risky asset. The case with riskless is only mentioned. However in chapter 6 there is an example with 3 risky asset plus a riskless (pag 98-99-100). The autors find the related tangency ptf and (max) Sharpe ratio. You can easily find the case with 2 risky asset plus riskless. $\endgroup$
    – markowitz
    May 20, 2016 at 13:47

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