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Lecture Investment analysis & portfolio management - Chapter 25

The expectation can now be employed to evaluate the expected return on an asset and a portfolio. This is achieved by introducing the idea of states of the world. A state of the world summarizes all the information that is relevant for the future return of an asset, so the set of states describes all the possible different future financial environments that may arise. Of course, only one of these states will actually be realized. These states of the world are the analysts way of thinking about, and modelling, what generates the randomness in asset returns. | Investment Analysis and Portfolio management Lecture: 25 Course Code: MBF702 Outline RECAP Expected returns Population variance Population covariance Choosing an investment portfolio Expected return The expectation can now be employed to evaluate the expected return on an asset and a portfolio. This is achieved by introducing the idea of states of the world. A state of the world summarizes all the information that is relevant for the future return of an asset, so the set of states describes all the possible different future financial environments that may arise. Of course, only one of these states will actually be realized. These states of the world are the analysts way of thinking about, and modelling, what generates the randomness in asset returns. Let there be M states of the world. If the return on an asset in state j is rj and the probability of state j occurring is πj. then the expected return on asset i is Example The temperature next year may be hot, warm or cold. The . | Investment Analysis and Portfolio management Lecture: 25 Course Code: MBF702 Outline RECAP Expected returns Population variance Population covariance Choosing an investment portfolio Expected return The expectation can now be employed to evaluate the expected return on an asset and a portfolio. This is achieved by introducing the idea of states of the world. A state of the world summarizes all the information that is relevant for the future return of an asset, so the set of states describes all the possible different future financial environments that may arise. Of course, only one of these states will actually be realized. These states of the world are the analysts way of thinking about, and modelling, what generates the randomness in asset returns. Let there be M states of the world. If the return on an asset in state j is rj and the probability of state j occurring is πj. then the expected return on asset i is Example The temperature next year may be hot, warm or cold. The returns to stock in a food production company in each of these states are given in the table. Example Consider a portfolio composed of two assets A and B. Asset A constitutes 20% of the portfolio and asset B 80%. The returns on the assets in the 5 possible states of the world and the probabilities of those states are given in the table. Population variance The population variance mirrors the interpretation of the sample variance as being the average of the square of the deviation from the mean. But where the sample variance found the average by dividing by the number of observations (or one less than the number of observations), the population variance averages by weighting each squared deviation from the mean by the probability of its occurrence. For a single asset the population variance is given by the expected value of the deviation from the mean squared, so As for the sample variance, the population variance is always non-negative. The population standard deviation is given by .