Calculate the expected future value if you instead took the $1,000 and invested in the risk-free option for 1 year. Would you prefer to invest in the alternative option, or the risk-free option? Explain. Is there an arbitrage opportunity? Explain.
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The bank offers risk-free, annual interest rates of 2%. You come across an alternative investment option costing $1,000 and offering $1,300 after 1 year. This investment has a 15% chance of failure and offering $0.
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- Which of the following statements is true? Select one of the options i. – iii.The future value of an investment (A) after two years with an annualcompound interest (i) isi. less than the future value of the investment (A) after two years withsimple interest (i)ii. equals to the future value of the investment (A) after two years withsimple interest (i)iii. greater than the future value of the investment (A) after two years withsimple interest (i).You are considering two alternative two-year investments: You can invest in a risky asset with a positive risk premium and returns in each of the two years that will be identically distributed and uncorrelated, or you can invest in the risky asset for only one year and then invest the proceeds in a risk-free asset. Which of the following statements about the first investment alternative (compared with the second) are true?a. Its two-year risk premium is the same as the second alternative.b. The standard deviation of its two-year return is the same.c. Its annualized standard deviation is lower.d. Its Sharpe ratio is higher.e. It is relatively more attractive to investors who have lower degrees of risk aversion.An investor must choose between two options. The first option (A) offers AED 10m for AED 2m a year for 5 years. The second optopm (B) offers AED 11m of AED 1m a year for four yeats and AED 7m in year 5. compare the present value of each option by assumong a range of the required rate of return of the investor say 8% 9% 10% 11% and 12% what is your advice?
- This question will compare two different arbitrage situations. Recall that arbitrage should equalize rates of return. We want to explore what this implies about equalizing prices. In the first situation, two assets, A and B, will each make a single guaranteed payment of $100 in 1 year. But asset A has a current price of $80 while asset B has a current price of $90.a. Which asset has the higher expected rate of return at current prices? Given their rates of return, which asset should investors be buying and which asset should they be selling?b. Assume that arbitrage continues until A and B have the same expected rate of return. When arbitrage ceases, will A and B have the same price?Next, consider another pair of assets, C and D. Asset C will make a single payment of $150 in one year while D will make a single payment of $200 in one year. Assume that the current price of C is $120 and that the current price of D is $180.c. Which asset has the higher expected rate of return at current…Suppose an investor shorts a straddle (a call option + a put option with the same strike price) with the following parameter values: S = 200, K = 250, σ = 0.30, RF = 0.05, q = 0, T = 5 years, and the interest rate, volatility, and the dividend yield are all given as annual values. Assuming that average daily returns are approximately zero, what is the 5% daily Delta-Gamma VaR of the short straddle position in dollars? Use 3 decimal places for your answer. (If you need to round the Gamma in an intermediate step, please use at least *6 digits*.)Consider a put option written on an underlying security that has a current value of $100 and has a volatility of 25% (i.e. .25). The put has a strike price of $100 and expires in 1 year. The risk-free rate is 3% (.03). If the time to expiration is changed from 1 to 2 to 3 years, what happens to the value of vega (the change in the put value given a percentage point change in the volatility – say from 25% to 26%)? (Note: vega is defined in note N16 on page 8; see ). What is the comparison of the change in vega (given a change from 1 to 2 to 3 years to expiration) if the strike price is $105 (relative to if the strike is $100)?
- In a binomial model, a call option and a put option are both written on the same stock. The exercise price of the call option is 30 and the exercise price of the put option is 40. The call option’s payoffs are 0 and 5 and the put option’s payoffs are 20 and 5. The price of the call is 2.25 and the price of the put is 12.25. a. What is the riskless interest rate? Assume that the basic period is one year. b. What is the price of the stock today?Ms. B has $1000 to invest. She is considering investing in the common stock of company M. In addition, Ms. B will either borrow or lend at the risk-free rate. Ms. B decide to invest $350 in common stock of company M and $650 placed in the risk- free asset. The relevant parameters are 1) What is the expected return? 2) What is the variance of the portfolio? 3) What is the standard deviation of the portfolio?Suppose the risk-free interest rate is 4.6%. Having $600 today is equivalent to having what amount in one year? (Round to the nearestcent.) Having $600 in one year is equivalent to having what amount today? (Round to the nearestcent.) Which would you prefer, $600 today or $600 in one year? Does your answer depend on when you need the money? Why or why not? (Round to the nearestcent.)
- I asked this question yesterday: Suppose that, in each period, the cost of a security either goes up by a factor of 2 or goes down by a factor of 1/2 (i.e. u=2, d=1/2). If the initial price of the security is 100, determine the no-arbitrage cost of a call option to purchase the security at the end of two periods for a price of 150. In the answer I got today the first step said: "We assume that the probability of moving up and moving down be 50% each, which means equal chances for both the movements. " I had learned that the risk neutral probability for the stock price to go up is: p=(1+r-d)/(u-d). In this particular problem, we'd have p=(1+0-.5)/(2-.5)=1/3. And so the probability going down would be 1-p or 2/3. Thus, my question is why weren't these probabilities used in the solution previously sent? And if they should be, what would be the new solution to the problem? Thank you for your help. I'm new to learning all of this and some of it is hard for me to understand.You are considering an investment that will pay you $1,200 in two year, $2,400 in three years and $3,600 in four years. If investors require a return of 8%, what price should it sell for? Question 7 options:Suppose you buy a one-year European call option on Apple with an exercise price of $100 and sell a one-year put option with the same exercise price. The current stock price is $100, and the interest rate is 10%. Draw a position diagram showing the payoffs from your investments. How much will the combined position cost you?