Assume you have created a 2-stock portfolio by investing $30,000 in stock X with a beta of 0.8, and $70,000 in stock Y with a beta of 1.2. Market risk premium is 8% and risk-free rate is 6%. The followings are the probability distributions of Stocks X and Y’s future returns:  State of Economy          Probability                  rx                      rY  Recession                      0.1                               -10%                -35% Below average              0.2                                 2%                   0% Average                        0.4                               12%                 20% Above average             0.2                               20%                 25% Boom                           0.1                               38%                 45% Calculate the portfolio’s expected rate of return and the standard deviation of its future returns Calculate the required rate of return of your portfolio. Which stock in your portfolio is currently under-valued? Explain.

Population Genetics In the study of population genetics, an important measure of inbreeding is the proportion of homozygous genotypesthat is, instances in which the two alleles carried at a particular site on an individuals chromosomes are both the same. For population in which blood-related individual mate, them is a higher than expected frequency of homozygous individuals. Examples of such populations include endangered or rare species, selectively bred breeds, and isolated populations. in general. the frequency of homozygous children from mating of blood-related parents is greater than that for children from unrelated parents Measured over a large number of generations, the proportion of heterozygous genotypesthat is, nonhomozygous genotypeschanges by a constant factor 1 from generation to generation. The factor 1 is a number between 0 and 1. If 1=0.75, for example then the proportion of heterozygous individuals in the population decreases by 25 in each generation In this case, after 10 generations, the proportion of heterozygous individuals in the population decreases by 94.37, since 0.7510=0.0563, or 5.63. In other words, 94.37 of the population is homozygous. For specific types of matings, the proportion of heterozygous genotypes can be related to that of previous generations and is found from an equation. For mating between siblings 1 can be determined as the largest value of for which 2=12+14. This equation comes from carefully accounting for the genotypes for the present generation the 2 term in terms of those previous two generations represented by for the parents generation and by the constant term of the grandparents generation. a Find both solutions to the quadratic equation above and identify which is 1 use a horizontal span of 1 to 1 in this exercise and the following exercise. b After 5 generations, what proportion of the population will be homozygous? c After 20 generations, what proportion of the population will be homozygous?

What term is used to express the likelihood of an event occurring? Are there restrictions on its values? If so, what are they? If not, explain.