# Question

Below we give a joint probability table for two utility bonds where the random variable x represents the percentage return for bond 1 and the random variable y represents the percentage return for bond 2.

In this table, probabilities associated with values of x are given in the row labeled p( x) and probabilities associated with values of y are given in the column labeled p( y). For example, P(x=9) .22 and P( y =11) .20. The entries inside the body of the table are joint probabilities— for instance, the probability that x equals 9 and y equals 10 is .08. Use the table to do the following:

a. Calculate µx , σx , µy , σy , and σ2xy.

b. Calculate the variance and standard deviation of a portfolio in which 50 percent of the money is used to buy bond 1 and 50 percent is used to buy bond 2. That is, find and σ29 and σp , where P =5x +5y. Discuss the risk of the portfolio.

In this table, probabilities associated with values of x are given in the row labeled p( x) and probabilities associated with values of y are given in the column labeled p( y). For example, P(x=9) .22 and P( y =11) .20. The entries inside the body of the table are joint probabilities— for instance, the probability that x equals 9 and y equals 10 is .08. Use the table to do the following:

a. Calculate µx , σx , µy , σy , and σ2xy.

b. Calculate the variance and standard deviation of a portfolio in which 50 percent of the money is used to buy bond 1 and 50 percent is used to buy bond 2. That is, find and σ29 and σp , where P =5x +5y. Discuss the risk of the portfolio.

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