1 / 20

Arbitrage Pricing Models

Arbitrage Pricing Models. Arbitrage Pricing Theory. Arbitrage - arises if an investor can construct a zero investment portfolio with a sure profit Since no investment is required, an investor can create large positions to secure large levels of profit

fauna
Download Presentation

Arbitrage Pricing Models

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Arbitrage Pricing Models

  2. Arbitrage Pricing Theory Arbitrage - arises if an investor can construct a zero investment portfolio with a sure profit • Since no investment is required, an investor can create large positions to secure large levels of profit • In efficient markets, profitable arbitrage opportunities will quickly disappear

  3. Example: Returns with Equal Probability

  4. Arbitrage Example

  5. E(r) P 25.83 D 22.25 s 6.40 8.58 Arbitrage Action and Returns Action: Short 3 shares of D and buy 1 of A, B & C to form portfolio P Returns: You earn a higher rate on the investment than you pay on the short sale

  6. Payoffs (short 300 shares of D. buy 100 shares of A. B & C each)

  7. Example - continued • What will happen in the market?

  8. APT & Well-Diversified Portfolios • F is some macroeconomic factor • For a well-diversified portfolio eP approaches zero • The result is similar to CAPM

  9. E(ri) = Expected Return U Underpriced asset Slope =  = risk premium RFR O Overpriced asset 0 Risk class of assets O and U Factor beta Arbitrage Pricing Theory Line

  10. E(r)(%) E(r)(%) F F Individual Security Portfolio Portfolio & Individual Security Comparison

  11. E(r)% 10 A D 7 6 C Risk Free = 4 Beta for F .5 1.0 Disequilibrium Example

  12. Disequilibrium Example • Short Portfolio C • Use funds to construct an equivalent risk higher return Portfolio D • D is comprised of A & Risk-Free Asset • Arbitrage profit of 1%

  13. E(r) M [E(rM) - rf] Market Risk Premium Risk Free Beta (Market Index) 1.0 APT with Market Index Portfolio

  14. APT and CAPM Compared • APT applies to well diversified portfolios and not necessarily to individual stocks • With APT it is possible for some individual stocks to be mispriced - not lie on the SML • APT is more general in that it gets to an expected return and beta relationship without the assumption of the market portfolio • APT can be extended to multifactor models

  15. A Two-Factor APT Model • The single factor APT can be extended to include more independent risk factors that work together to determine market prices • APT is more flexible than SML • However, APT offers no clues as to what factors are relevant • Research must be done to determine best explanatory factor

  16. Three Highly Diversified Portfolios • Three risk-averse investors form portfolios B, C and D (each contains N assets) with two risk factors • These are arbitrage portfolios, requiring no cash investment • When N is large, unsystematic residual risk is diversified away

  17. Three Highly Diversified Portfolios • The general form of the APT model with two factors is: • The specific APT model for the three portfolios on the previous slide is:

  18. The Arbitrage Portfolio • Consider a mispriced asset • Portfolios S and U have the same risk but different expected returns • Portfolio U is underpriced • Smart investors would buy portfolio U

  19. The Arbitrage Portfolio • It is possible to set up a perfect hedge with portfolios S and U to create a riskless profit opportunity

  20. The k-Dimensional APT Hyperplane • A more elaborate model with k risk factors is: • Salomon Smith Barney uses a multi-factor arbitrage pricing model including factors such as: • The market’s trend or drift • Economic growth • Credit quality • Interest rates • Inflation shock • Small-cap premiums

More Related