Variance means how much uncertainty o Variance means Principal X Rate X Time. O Variance means how much VIX or volatilin means how much bonds return. Variance
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- Is co-variance a measure of relative risk, or absolute risk? A relative risk, because it is linked with the performance(s) other asset(s). B absolute risk, because it is not linked with the performance(s) other asset(s). relative risk, because it measures the co-movement of two assets. absolute risk, though it measures the co-movement of two assets.A stock has a correlation with the market of .45. The standard deviation of the market is 21%, and the standard deviation of the stock is 35%. a. What is the covariance between the market and the stock? b. Calculate the stock beta.RISK ANALYSIS A financial investor builds a portfolio that is worth an expected £35mil. The investor knows that his analysts can build a model to boost the potential return from the portfolio investment. The additional return has a Normal Distribution with mean £3mil and standard deviation £0.5mil. The investor wishes to sell his financial services at a price that guarantees his expected profit will be 5% of the total return from the portfolio. What should the price of his financial service be? Simulate (with a min of 200 repetitions) the average and the standard deviation of the profit the financial advisor realizes when setting the price for his services between 1% and 10% of the total expected return from the portfolio. Then discuss your findings.
- Economics Consider a supplier that manufactures a product at $2 per unit and sells them to retailers at $7 per unit. The retailer sells each product to the end consumer at $10. At this retail price, market demand is normally distributed, with a mean of 1,000 and a standard deviation of 300. The supplier agrees to buy back unsold products for $b even though any leftover product at the end of sale period are worthless. a) What is the retailer's order quantity under local optimization when b=0? b) What is the optimal order quantity under global optimization? Round up to the nearest integer. Derive the optimal value of b. c) With the optimized value of b in the buyback clause, how many discs should an independent retailer order? Round up your solution to the nearest integer. d) What is the expected overstocking given the optimized value of $b? What is the expected understocking given the optimized value of $b? What is retailers' expected profit? What is the manufacturer's expected profit?An insurer has a pool of identical policyholders each with a potential claim that fits the ideal characteristics of insurability. There are 10,000 policyholders in the pool. Any single policyholder has an expected claim of 10 and the claim’s standard deviation is 2. The insurer collects premiums at the beginning of the year, and pays claims at the end of the year. Premium is 9.5 per insurer. The insurer invests premiums at an annual rate of 5.68 percent. What is the probability (a very close approximation will suffice) that the insurer will not have sufficient money to pay claims?Uncertainty The Utility function is U = W1/3Flood occurs with Probabilities=1/25. The Value of a house is $450,000 if no flood. Aftera flood, the value is $50,000. Cost of insurance is 10 cents per dollar.a. Calculate EU b. Calculate EV c. Calculate CE d. Calculate RP e. Calculate the variance and standard deviation f. How much insurance should you buy? Assume your are paying premium in all events.g. What is the expected profit of the insurance company? h. Calculate the coefficient of absolute and relative risk aversion
- Consider an investment that pays off $700 or $1,600 per $1,000 invested with equal probability. Suppose you have $1,000 but are willing to borrow to increase your expected return. What would happen to the expected value and standard deviation of the investment if you borrowed an additional $1,000 and invested a total of $2,000? What if you borrowed $2,000 to invest a total of $3,000? Instructions: Fill in the table below to answer the questions above. Enter your responses as whole numbers and enter percentage values as percentages not decimals (.e., 20% not 0.20). Enter a negative sign (-) to indicate a negative number if necessary. Invest $1,000 Invest $2,000 Invest $3,000 Expected Value Percent Increase Standard Deviation 1150 S 28 % $ 8 % $ Expected Return N/A Doubled Tripled : #You plan to invest $1,000 in a corporate bond fund or in a common stock fund. The following table represents the annual return (per $1,000) of each of these investments under various economic conditions and the probability that each of those economic conditions will occur. Compute the expected return for the corporate bond and for the common stock fund. Show your calculations on excel for expected returns. Compute the standard deviation for the corporate bond fund and for the common stock fund. Would you invest in the corporate bond fund or the common stock fund? Explain. If choose to invest in the common stock fund and in (c), what do you think about the possibility of losing $999 of every $1,000 invested if there is depression. Explain.What is the risk premium(s)?
- Explain why the variance of an investment is a useful measure of the risk associated with itSuppose one uses the single-index model to estimate characteristics of securities.Which of the following statements is correct? (a)The covariances between securities are the same as in the data. (b)The variance of a portfolio is the same as in the data. (c)The expected return and the variance of a security are the same as in the data. (d)The expected return,variance and covariances of a security are the same as in the da1. The following table gives the PDF (Probability Density Function) of the discrete variable X X -1 -2 2 3 4 f(x) 0.1 0.2 0.1 0.3 0.1 0.2 Calculate the E(x) (expectation) and var(x) (variance) 2. Prove the following properties of expectation and variance: If a and b are constants, X and Y are random variables, then E(aX+b)=aE(x)+b var (aX+ b) = a² var (X) var (X+ Y)= var (X) + var (Y) +2 cov(X, Y) =var (X) + var (Y) + 2pox0y Of which p is correlation coefficient, oz and o, are standard error of X and Y. 3. Assume that X- N(6, 4). What is the probability that 2 10?