Concept explainers
(A)
Adequate Information:
The
To calculate:
The fraction of the portfolio, fraction in equity and the stock portfolio if falls by 3%.
Introduction:
Portfolio involves financial asset grouping viz. currencies, commodities, bonds, stocks and cash equivalents. It also comprises of fund counterparts such as closed funds, exchange traded funds and mutual funds. Non-publicly tradable securities such as private, art and real estate investment are also part of portfolios.
Explanation of Solution
Fractions of portfolio invested in T-bills and equity can be calculated based on the Black-Scholes
model. The value of
to T-bills and equity can be known for value of
Formula for
Substitute values to calculate
Calculate the Black-Scholes hedge ratio
"NORMSDIST" function are as follows:
- First, go to the Menu bar of Excel and select 'Formulas' option
- Select Insert Function '(fx)
- Then select a category as Financial
- Then select "NORMSDIST" and click OK
- Then the Function Argument window will open. Now, input the given data in the required field
- Click OK
- The formula will display the final answer as 0.7422
Therefore,
Calculate the put delte as follows:
Hence, place 25.785 of the portfolio in T-bills and 74.22%
Hence, place 25.785 of the portfolio in T-bills and 74.22%
(B)
Adequate information:
To calculate:
Fractions of portfolio divided into bills and equity If stock prices fall by 3% on the first day of trading. It means
Introduction:
Portfolio involves financial asset grouping viz. currencies, commodities, bonds, stocks and cash equivalents. It also comprises of fund counterparts such as closed funds, exchange traded funds and mutual funds. Non-publicly tradable securities such as private, art and real estate investment are also part of portfolios.
Explanation of Solution
Fractions of portfolio invested in T-bills and equity can be calculated based on the Black-Scoles model. The value of
Substitute values to calculate
Calculate the Black-Scholes hedge ratio
Hence,
Calculate the put delta as follows:
Hence, place 27.79% of the portfolio in T-bills and 72.21%
Want to see more full solutions like this?
Chapter 21 Solutions
INVESTMENTS(LL)W/CONNECT
- What makes for a good investment? Use the approximate yield formula or a financial calculator to rank the following investments according to their expected returns. Buy a stock for $30 a share, hold it for three years, and then sell it for $60 a share (the stock pays annual dividends of $2 a share). Buy a security for $40, hold it for two years, and then sell it for $100 (current income on this security is zero). Buy a one-year, 5 percent note for $1,000 (assume that the note has a $1,000 par value and that it will be held to maturity).arrow_forwardSuppose you have $100,000 in cash, and you decide to borrow another $25,000 at a 6% interest rate to invest in the stock market. You invest the entire $125,000 in a portfolio J with a 24% expected return and a 26% volatility. What is the expected return and volatility (standard deviation) of your investment? What is your realized return if J goes up 13% over the year? What return do you realize if J falls by 26% over the year?arrow_forwardSuppose you have $275,000 in cash, and you decide to borrow another $33,000 at a 4% interest rate to invest in the stock market. You invest the entire $308,000 in a portfolio J with a 15% expected return and a 22% volatility. a. What is the expected return and volatility (standard deviation) of your investment? b. What is your realized return if J goes up 32% over the year? c. What return do you realize if J falls by 25% over the year?arrow_forward
- An invester has up to $250,000 to inveest in three types of investments. Type A pays 8% annually and has a risk factor of 0. Tupe B pays 10% annually and has a risk factor of 0.06. Type C pays 14% annually and has a risk factor of 0.10. to have a well-balanced potfolio, the investor imposes the following conditions. The average risk factor should be no greater than 0.05. Moreover, at least one-fourth of the total portfolio is to be allocated to type A investments ans at least one-fourth of the portfolio to be allocated to type B investments. How much should be allocated to each type of investment to obtain a maximum return? Use simplex method to solve this.arrow_forwardAs a junior investment manager, your boss instructs you to help a client to invest $100,000 for the next year. Particularly, you are asked to form an investment portfolio for the client by investing in risk-free assets like 90-day bank bill and two stocks: A and B. Stock A has a beta value of 0.8, an expected return of 7% and a standard deviation of 10%; and stock B has a beta value of 1.2, an expected return of 12% and a standard deviation of 15%. The correlation coefficient between the returns for the two stocks is 0. The risk-free rate is 2%. (a) What is the expected return of the risky portfolio with the two stocks that has the least amount of risk? (b) Suppose that the optimal risky portfolio with the two stocks has a weight of 53% in A and 47% in B, and has the expected return of 9.4% and standard deviation of 8.8%. If this client is willing to take a risk measured by standard deviation of 5% for his overall investment portfolio, how much would you recommend to the client to…arrow_forwardAs a junior investment manager, your boss instructs you to help a client to invest $100,000for the next year. Particularly, you are asked to form an investment portfolio for the clientby investing in risk-free assets like 90-day bank bill and two stocks: A and B. Stock A hasa beta value of 0.8, an expected return of 7% and a standard deviation of 10%; and stockB has a beta value of 1.2, an expected return of 12% and a standard deviation of 15%.The correlation coefficient between the returns for the two stocks is 0. The risk-free rate is2%.(a) What is the expected return of the risky portfolio with the two stocks that has theleast amount of risk?(b) Suppose that the optimal risky portfolio with the two stocks has a weight of 53% inA and 47% in B, and has the expected return of 9.4% and standard deviation of8.8%. If this client is willing to take a risk measured by standard deviation of 5% forhis overall investment portfolio, how much would you recommend to the client toinvest in the…arrow_forward
- A fund manager has a well-diversified portfolio that mirrors the performance of the S&P 500and is worth $240 million. The value of the S&P 500 is 4,800, and the portfolio manager wouldlike to obtain insurance against a reduction of more than 3% in the value of the portfolio over thenext four months. The risk-free interest rate is 6% per annum. The dividend yield on both theportfolio and the S&P 500 is 4%, and the volatility of the index is 35% per annum. What amount(in dollars) of the portfolio should be sold and kept in risk-free securities for portfolio insurance?arrow_forwardJulie is the portfolio manager at know better plc. She wants to estimate the interest rate risk of assets of the company consisting of 1 million shares of Bond A, 2 million shares of Bond B, and 2 million shares of Bond C. The duration of Bond A is 5.59, a valuation model found that if interest rates decline by 30 basis points, the value of Bond A will increase to 83.5 pounds, and if interest rates increase by 30 basis points, the value of Bond to A will decline to 80.75 pounds. The same valuation model also found that if interest rates decreases by 50 basis points, the value of Bond B increases to 104.6 pounds, and if interest rates increases by 50 basis points, the value of Bond B decreases to 96.4 pounds, and the current value of Bond B is 100 pounds. Kirstin also knows from the valuation model that, by using the duration and convexity rule, if interest rates decline by 1%, the price of bond C increases approximately by 8.46 pounds, and if interest rates increase by 3%, the price of…arrow_forwardSuppose that a portfolio management company manages an investment fund. The fund manager observes a bond in the market and intends to add it to the fund portfolio. The bond has a $100.000 par value, 10% coupon rate (coupon payments are annual) and a 2-years maturity. The business model is to “hold-until-maturity”. The company purchases the bond at the beginning of the year when the market yields are 12%. After exactly 1 year of investment, market yields increase to 14%. What would be the approximate profit or loss amount in the income statement for that 1-year period? A) $ 1,594 loss B) $ 1,723 lossC) $ 9,871 profit D) $ 10,191 profitE) Other (please specify)arrow_forward
- F generates a single cash-flow in one year. This cash-flow depends on the strategy chosen by the management: The safe strategy yields a certain cashflow of $3,500, The risky strategy yields a high cashflow of $15,000 with probability 0.2, and a low cash-flow of $625 with probability 0.8. F has 3 stocks outstanding and one bond with a $2,000 face value, a 5% annual coupon and a one-year maturity. All agents are risk neutral and the risk free rate is 5%. 1) If the bond is convertible with a conversion ratio of 4, which strategy does the management choose and why? In what cases do the bondholders convert in what cases do they not convert (they can see the cashflow before converting)?arrow_forwardYou are trying to sell a mutual fund to a customer, who can tolerate losing more than 10% of assets during a bad year if that happened only once every twenty years. If the expected annual return of the fund you are selling is 8% and the daily volatility is 0.72%, explain briefly how likely is it that the customer would buy the fund. Assume that there are 255 trading days in a year.arrow_forwardSuppose that a portfolio management company manages an investment fund. The fund manager observes a bond in the market and intends to add it to the fund portfolio. The bond has a 100.000 TL par value, 10% coupon rate (coupon payments are annual) and a 2-years maturity. The business model is to “hold-until-maturity”. The company purchases the bond at the beginning of the year when the market yields are 12%. After exactly 1 year of investment, market yields increase to 14%. What would be the approximate profit or loss amount in the income statement for that 1-year period? A) 1.723 TL loss B) 10.191 TL profit C) 9.871 TL profit D) 1.594 TL loss E) OTHERarrow_forward
- Pfin (with Mindtap, 1 Term Printed Access Card) (...FinanceISBN:9780357033609Author:Randall Billingsley, Lawrence J. Gitman, Michael D. JoehnkPublisher:Cengage LearningIntermediate Financial Management (MindTap Course...FinanceISBN:9781337395083Author:Eugene F. Brigham, Phillip R. DavesPublisher:Cengage Learning
- EBK CONTEMPORARY FINANCIAL MANAGEMENTFinanceISBN:9781337514835Author:MOYERPublisher:CENGAGE LEARNING - CONSIGNMENT