Ralph Vince - Portfolio Mathematics
214 THE HANDBOOK OF PORTFOLIO MATHEMATICS Converting these to outcomes yields: Toss# 123 2 2 − 1 2 2 − 1 − 1 2 2 − 1 − 1 2 − 1 − ...
Laws of Growth, Utility, and Finite Streams 215 taken to the root of 1/n, wherenequals the number of HPRs, or tosses, in this ca ...
216 THE HANDBOOK OF PORTFOLIO MATHEMATICS 3.Since all streams are finite in length, regardless of how long, we will al- ways be ...
Laws of Growth, Utility, and Finite Streams 217 FIGURE 6.2 Optimalfas an asymptote the fact that what we are calling the optimal ...
218 THE HANDBOOK OF PORTFOLIO MATHEMATICS explanation for investor preferences. However, I strongly feel that if an in- vestor’s ...
Laws of Growth, Utility, and Finite Streams 219 constant (added, subtracted, multiplied, or divided) will result in the same inv ...
220 THE HANDBOOK OF PORTFOLIO MATHEMATICS FIGURE 6.3 Three basic types of utility functions 4.The fourth characteristic of utili ...
Laws of Growth, Utility, and Finite Streams 221 5.The fifth characteristic of utility preference functions pertains to how the p ...
222 THE HANDBOOK OF PORTFOLIO MATHEMATICS maximizersand evolution; hence, Wentworth calls his thesurvival hy- pothesis.A thumbna ...
Laws of Growth, Utility, and Finite Streams 223 Let’s suppose you expect, in the best case, to win $5,000 on a trade, and lose $ ...
224 THE HANDBOOK OF PORTFOLIO MATHEMATICS You should complete the table for the certainty equivalent columns. For instance, when ...
Laws of Growth, Utility, and Finite Streams 225 FIGURE 6.4 Example utility function outcome, and one forworst outcomeas well. Su ...
226 THE HANDBOOK OF PORTFOLIO MATHEMATICS in your decisions. Usually, scattering is more pronounced near the extremes (left and ...
Laws of Growth, Utility, and Finite Streams 227 three plays, three holding periods, we would maximize growth by betting .37868 o ...
228 THE HANDBOOK OF PORTFOLIO MATHEMATICS But what if a win of $2 were only one-and-a-half times as valuable to us as a loss of ...
Laws of Growth, Utility, and Finite Streams 229 value, which will then yield a nonuniform optimalfvalue (one whose value changes ...
230 ...
CHAPTER 7 Classical Portfolio Construction Modern Portfolio Theory Recall from Chapter 4 the paradox of the optimalfand a market ...
232 THE HANDBOOK OF PORTFOLIO MATHEMATICS parameters change quite quickly from one time period to another, optimal portfolio mix ...
Classical Portfolio Construction 233 FIGURE 7.1 A portfolio of two positively correlated market systems—a poor choice FIGURE 7.2 ...
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