We define a metric to measure options returns from the seller point of view, write an algorithm that simulates the sale of options and collects premiums of at-the-money european options at ex-ante market real prices (inflow of money to the seller of options), hold these contracts open until the original expiration, calculates the ex-post payoffs (outflow of money for the seller in case the option ends up in the money) and with that data calculating a

realized return.

In equation (5), [R.sup.i.sub.t+k] is the

realized return on a stock or portfolio i from time t to t+k.

In addition, businesses that implement fleet tracking typically

realized return on investment in as little as one month.

Measure 2 more closely aligns income and wealth by excluding these items, but may underestimate the

realized return on capital for decedents whose businesses paid them a salary.

The marginal distribution of return on A always dominates the corresponding distribution on B, and the only rationale for allocating funds to the second asset (B) follows from the possibility that

realized return on A would be low when the return on B is high; that is, from nonperfect correlation in returns.

In Equations (7) to (10) [R.sub.i,t] is the

realized return on stock i in month t, [logME.sub.i,t-1] is the natural logarithm of market equity for firm i in month t - 1, log([BE.sub.i,t-1]/[ME.sub.i,t-1]) is the natural logarithm of the ratio of book value of equity to market value of equity for firm i in month t - 1, [[beta].sup.realized.sub.i,t-1] is the lagged realized beta of stock i in month t - 1, and [[beta].sup.AR.sub.i,t|t-1], [[beta].sup.MA.sub.i,t|t-1], and [[beta].sup.GARCH.sub.i,t|t-1] are the conditional expected beta of stock i in month t estimated with the information set at month t - 1.

Specifically, over the last few years a very active research agenda into the direct (model-free) measurement of the

realized return variation and covariation of financial assets at daily or even higher intraday frequencies has developed.

Mayo spent between $5.5 million and $6 million when it implemented the system a decade ago, according to clinic officials, and

realized return on the initial investment within five years.

Eighty-five percent of respondents indicated they view risk management as an investment, in particular because they believe it protects their business continuity and there is a

realized return on investment.

Simulation results, by converging to the average

realized return over that particular sample period, obscure these unpleasant possibilities.

Since each observation has an equal probability of occurrence, each

realized return is assigned a probability of 1/762.

This occurs because the cross-sectional distribution of security returns is right-skewed, and the size-adjusted returns are measured as the difference between the

realized return and the mean return for all stocks in the same market capitalization decile.