Editing Modern portfolio theory (section)

===Two mutual fund theorem===

One key result of the above analysis is the [[Mutual fund separation theorem#No risk-free asset|two mutual fund theorem]].<ref name="Merton">{{Cite journal |last=Merton |first=Robert C. |date=September 1972 |title=An Analytic Derivation of the Efficient Portfolio Frontier |url=http://dx.doi.org/10.2307/2329621 |journal=The Journal of Financial and Quantitative Analysis |volume=7 |issue=4 |pages=1851–1872 |doi=10.2307/2329621 |jstor=2329621 |issn=0022-1090 |archive-url=https://web.archive.org/web/20220321184804/http://www.stat.ucla.edu/~nchristo/statistics_c183_c283/analytic_derivation_frontier.pdf |archive-date=21 Mar 2022|hdl=1721.1/46832 |hdl-access=free }}</ref><ref>{{cite journal |jstor=3689808 |ssrn=1086184|title=Explicit Solution of a General Consumption/Investment Problem|last1=Karatzas|first1=Ioannis|last2=Lehoczky|first2=John P.|last3=Sethi|first3=Suresh P.|last4=Shreve|first4=Steven E.|journal=[[Mathematics of Operations Research]]|year=1986|volume=11|issue=2|pages=261–294|doi=10.1287/moor.11.2.261|s2cid=22489650}}</ref>  This theorem states that any portfolio on the efficient frontier can be generated by holding a combination of any two given portfolios on the frontier; the latter two given portfolios are the "mutual funds" in the theorem's name.  So in the absence of a risk-free asset, an investor can achieve any desired efficient portfolio even if all that is accessible is a pair of efficient mutual funds. If the location of the desired portfolio on the frontier is between the locations of the two mutual funds, both mutual funds will be held in positive quantities. If the desired portfolio is outside the range spanned by the two mutual funds, then one of the mutual funds must be sold short (held in negative quantity) while the size of the investment in the other mutual fund must be greater than the amount available for investment (the excess being funded by the borrowing from the other fund).