B.3 Portfolio Theory II-1-1.pptx

B.3 Portfolio Theory II-1-1.pptx - 1 Outline Portfolio...

Info icon This preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
1 Outline: Portfolio Theory II Add a risk-free asset to the two risky asset model Identify portfolios that combine risky and risk-free assets The new frontier is linear Slope is the Sharpe ratio Identify the optimal portfolio of risky assets – the tangency portfolio Determining the optimal complete portfolio Generalize to N assets (Markowitz model) Efficient portfolios Optimal complete portfolio All investors hold same portfolio of risky assets Mutual fund theorem Asset allocation in the real world Assessing risk preferences Venti Portfolio Theory II
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Review: The efficient frontier with two risky securities Venti Portfolio Theory II 2 . Portfolio B Frontier shows all possible combinations of risk and return available to investors holding varying amounts of risky portfolios B and S (without short-selling) Portfolio S . . Efficient frontier
Image of page 2
Next: Two Extensions Venti Portfolio Theory II 3 1. Add the risk-free asset to the mix What is the optimal portfolio of risky assets? What is the optimal complete portfolio (including both risky and risk-free assets)? 2. Generalize from 2 risky securities (a stock fund and a bond fund) to N risky securities (many stocks and many bonds)
Image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Venti Portfolio Theory II 4 Add a Risk-Free Asset to the Portfolio Risk-Free Asset : Assume return is r f =5%, f =0.0 Can borrow and lend at this rate We can combine the risk-free asset with any of the portfolios we have constructed from stocks and bonds. Consider an arbitrarily chosen portfolio of risky assets P Let r c denote the return on a portfolio that combines the risk-free asset and portfolio P. Then: (1) E(r c ) = E(r P ) + (1- )r f (2) c = P where is the share held in the portfolio of risky assets.
Image of page 4
Possible Capital Allocations with Stocks, Bonds and T-bills Venti Portfolio Theory II 5 CAL P . Portfolio P r f =5% CAL: Capital Allocation Line: Opportunity set with risky portfolio P and risk-free asset
Image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Substitute (2) into (1) and rearrange to yield: What is the slope of the CAL? Venti Portfolio Theory II 6 P f C C f P ff C P P E r r σ E r =r E r r = σ σ P f P E r -r Slope= Sharpe Ratio σ
Image of page 6
Optimal Portfolio of Risky Assets Venti Portfolio Theory II 7 Which portfolio of risky assets is optimal? Maximize the slope of the CAL (the Sharpe ratio) for any possible portfolio, P Ans. When it is just tangent to the efficient frontier. The optimal portfolio of risky assets (stocks and bonds) is the tangency portfolio T When is At a maximum? p f p p E r -r S = σ
Image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Opportunity Set with Stocks, Bonds and a Risk-Free Asset Venti Portfolio Theory II 8 CAL T . Portfolio T (r T =11%, s T =14.2%)
Image of page 8
Let w B be the share in bonds and (1-w B ) in stocks Substitute the following into the Sharpe ratio: E(r P ) = w B E(r B ) + w S E(r S ) p 2 = w B 2 B 2 + w S 2 S 2 + 2w B w S BS B S Maximize S P w/r/t w B to obtain: Aside: Calculating the Optimal Risky Portfolio Venti Portfolio Theory II 9 2 B f S s
Image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 10
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern