The judge return from investing in a security over some future attribute period is an estimate of the future outcome of this security.
Although the Expected Return is an estimate of an investors expectations of the future, it can be estimated using either ex ante (forward looking) or ex post (historical) data.
If the expected return is equal to or greater than the required return, buy the security.
Regardless of how the individual returns are calculated, the Expected Return of a Portfolio is the weighted sum of the individual returns from the securities making up the portfolio:
Ex ante expected return computations are based on probabilities of the future takes of nature and the expected return in to each one state of nature. Sum over all states of nature, the product of the luck of a state of nature and the return projected in that state.
StatePsRsPs * Rs
Good30%20%0.3(0.2)
Average50%15%+0.5(0.15)
Poor20%-4%+0.2(-0.04)
12.70%
Ex post expected return calculations are based on historical data. Add the historical returns and then divide by the number of observations.
YearRt
200215%
200320%
20049%
200510%
20065%
11.
80%
Variance (Standard Deviation): ?2 (?)
Variance is a pulsation of the dispersion in outcomes around the expected value. It is used as an indication of the risk inherent in the security. Standard discrepancy is the square root of variance.
Ex ante variance calculation:
1.The expected return is subtracted from the return within each state of nature; this dissimilarity is then shape.
2.Each squared difference is multiplied by the probability of the state of nature.
3.These weighted squared terms are then summed together.
StatePsRsPs * Rs(Rs E(R))2 * Ps
Good30%20%0.3(0.2)0.3(0.2-0.127)2
Average50%15%+0.5(0.15)+0.5(0.15-0.127)2
Poor20%-4%+0.2(-0.04)+0.2(-0.04-0.127)2
12.70%0.00748.63%
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