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... ( 18. 18) Given the above results, the set of expected returns and standard deviations of returns are asindicated in Figures 18. 6 and 18. 7. 18. 4 Zero-Covariance Frontier ReturnsSince the set of ... kq(Figure 18. 8). 18. 7.1 ExampleIn Example 18. 3.1, the pricing kernel kqequals (1, 1/2, 3/2) and its standard deviation isσ(kq) =1√6. ( 18. 33)The risk-free return ¯r equals 1 and the Sharpe ... standarddeviations of frontier returns are shown in Figures 18. 3 and 18. 4.If the expectations kernel is risk free, then E(re) equals the risk-free return ¯r; and as followsfrom 18. 10, the expectation of...

... Journal of Mathematical Economics, 22:463–4 78, 1993.[2] J. Michael Harrison and David M. Kreps. Martingales and arbitrage in multiperiod securitiesmarkets. Journal of Economic Theory, 20: 381 –4 08, ... Results of Duffie and Shafer [2] (see also Duffie [1]) imply that for a generic set of agents’ endowments and securities’ dividends an equilibrium exists.2 28 CHAPTER 23. DYNAMICALLY COMPLETE MARKETS and q(ξt) ... adate-1 payoff of 1 .8 if the first report is good and 0 .8 if the first report is bad—as needed to financethe date-1 holdings. The date-0 price of this portfolio strategy is 1.02.The payoff of this portfolio...