# Daily Archives: November 16, 2020

## Create a plan for interpreting and judging the data, and making recommendations.

1.       How and where will data be recorded?

2.       Create a plan for interpreting and judging the data, and making recommendations.

3.       How will a record of the evaluation efforts and subsequent curriculum alterations be maintained?

4.       When, how, and to whom will data, evaluation results, and recommendations be reported?

5.       Develop a plan for review of the evaluation process

6.       Describe any faculty development needed to support curriculum evaluation. What is the basis of this assessment?

## Calculate the price of each bond in the following scenarios

Price sensitivity and convexity. It is recommended to use a spreadsheet to solve this problem.

Suppose the US zero-coupon rate curve is given as:

Consider the following three bonds with face value \$100:

(a) Calculate the arbitrage price of each bond.

(b) The price sensitivity of a bond (also known as the ‘dollar value of one basis point’ or DV01) is defined

as the change in price when all rates go up 1 basis point (i.e. a +0.01%

parallel shift of the entire zero-coupon rate curve). Compute the price sensitivity of each bond.

(c) Calculate the price of each bond in the following scenarios:

(i) 10 basis point rate increase (+0.10%);

(ii) 1 point rate increase (+1%).

….

Zero-coupon rate curve and expectations. The short-term zero-coupon rate curve of the euro zone is given as:

The current refinancing rate of the European Central Bank (ECB) is at 2.75%. This is the rate at which banks can borrow from the ECB for 2 weeks. The ECB Board of Governors will meet in 2 weeks and potentially decide on a new refinancing rate R.

(a) Without making any calculation can you guess if the market expects the ECB to:

(i) Lower its rate by 25 bps (i.e. R = 2.5%)?

(ii) Leave its rate unchanged (i.e. R = 2.75%)?

(iii) Raise its rate by 25 bps (i.e. R = 3%)?

(iv) Raise its rate by 50 bps (i.e. R = 3.25%)?

(v) Any other scenario?

(b) The….

## True or False? The three questions are independent.

True or False? The three questions are independent.

(a) “The average monthly return of Kroger Co. in 2009-10 was 0.28% (including dividends). Therefore, its

annual return was (1 + 0.28%)12 − 1 ≈ 3.4%.”

(b) “To calculate the annual volatility of a series of monthly returns I may either compute their standard

deviation and multiply it by  or equivalently I may annualize each monthly return and then compute the corresponding standard deviation.”

(c) “The return of my portfolio is 15% per year and its risk is 25% per year. The stock of MeToo.Com has a 15% return and 30% risk. Hence, adding MeToo.Com to my portfolio would increase its risk but not its return.”

## What is the realized risk-return profile of Richky Corp.?

a.Risk-free rate and Sharpe ratio Using the data for the Treasury bond in determine the theoretical risk-free rate rf so that the Sharpe ratio of the T-Bond be equal to 1.

b: Risk and return of Richky Corp. The table below gives the stock price of Richky Corp. at the end of

each month over the past year. The risk-free rate was constant at 5%.

(a) Given a \$134 initial stock price at the end of the previous year and a \$13 dividend per share distributed on 30 June, calculate the monthly returns of Richky Corp. Assume that the dividend is reinvested in the stock.

(b) What is the realized risk-return profile of Richky Corp.?

(c)  You are the Chief Financial Officer of Richky Corp. At a….

## Which portfolio would you choose to obtain an expected return around 5.25%?

Currency portfolio. It is recommended that you solve this problem using a spreadsheet. You are a euro-zone investor with 1 billion euros to be invested in dollars (USD), yen (JPY), or pounds sterling (GBP). You are given the following market data and forecasts:

(a) Plot the three currencies on a risk-return chart, taking the interest produced by each currency into account.

(b) Draw the risk-return evolution of a portfolio which gradually switches from dollars to yen (i.e. 100% in dollars initially, then 90% in dollars and 10% in yen, etc.). Repeat this question for a portfolio which gradually switches from yen to pounds, and then from pounds to dollars.

(c) Plot the risk-return profiles of all possible portfolios made of the three currencies, considering only long investment….

## What is the payoff at maturity of a portfolio long a zero-coupon bond with face value \$90 and an in-the-money European call option struck at \$90 on an underlying stock S currently trading at \$100?

Option payoffs. The three questions are independent.

(a) In each of the three examples in identify the underlying assets, the maturity date, and the payoff formula.

(b) Find a portfolio of European options on an underlying asset S with maturity T whose payoff matches the figure below:

(c) What is the payoff at maturity of a portfolio long a zero-coupon bond with face value \$90 and an in-the-money European call option struck at \$90 on an underlying stock S currently trading at \$100? Assuming no dividends, no arbitrage, infinite liquidity, and the ability to short-sell, show that this portfolio must be worth more than \$100.

## Do you think barrier options should be more expensive than plain vanilla options of same characteristics?

Barrier option A ‘knock-out barrier option’ is a call or put option which may only be exercised at maturity if the price of the underlying never hits a pre-agreed barrier price H throughout the life of the option. Symmetrically, a ‘knock-in barrier option’ may only be exercised at maturity if the price of the underlying hits the barrier price H.

(a) Do you think barrier options should be:

(i) more expensive than plain vanilla options of same characteristics?

(ii) less expensive than plain vanilla options of same characteristics?

(iii) more expensive in some cases and less expensive in other cases? (Please specify.)

(b) In this question we consider calls with strike 100 and 1-month maturity. The underlying spot price is

## What is the 1-year forward exchange rate?

Forward exchange rate. This problem is about forward contracts in foreign exchange and goes beyond the scope of equity derivatives. The spot exchange rate of the euro is S dollars, i.e. to buy one euro one must pay S dollars. The euro zone yield curve is flat at rEU while the American yield curve is flat at rUS. A forward contract on the euro-dollar is an agreement to receive euros and pay dollars at a pre-agreed date T and exchange rate F.

(a) Starting with €1, find two ways to have dollars in a year’s time by investing or borrowing in either currency and exchanging between currencies through the spot and forward markets. Using an arbitrage argument, establish that the 1-year forward exchange rate of the euro must….

## Find an upper bound for z(T) as a function of T, τ and z(T + τ ).

Forward interest rate. This problem is about forward interest rates and goes beyond the scope of equity derivatives. Consider a market with no arbitrage and infinite liquidity where investors can lend and borrow money for any maturity T at the zero-coupon rate z(T). Let z(T, τ ) denote the forward rate agreed today on a loan beginning at time t = T and ending at time t = T + τ . For instance, the ‘6-month × 1-year’ forward rate z(0.5, 1) is the rate agreed today on a loan starting in six months and ending in eighteen months.

(a) In this question the zero-coupon rate curve is given as: z(T) = 5% + T × 0.5%.

(i) Draw z(T) as a function of maturity T.

(ii) Suppose….