SBS Finance Assignment Help With Solution
1 – Duration of a bond
I came across the following news earlier this week regarding the “risk-free” reference rate (it was part of a Blog by Bill Bonner, a great finance blogger). The German government has a bond outstanding with a 2.5% coupon that matures in August 2046. Since mid-April, the yield of this bond has risen by just over 1 percentage point, from 0.46% to 1.54% by now (mid June).
a. Calculate the approximate price of the bond in mid-April 2015 and in mid-June, 2015 and the change over the period. How does the change seem to you?
b. What is the duration of the bond now (mid-June 2015). Please calculate manually/spreadsheet (vs just using Excel Formula function; you may use it to check)
c. What would be the expected price change of the bond if yields were to go up from here another 10 bps (from 1.54% to 1.64%). Use your duration model to calculate that and verify it (either by using an excel formula or recalculating your spreadsheet).
d. How could a trader hedge against such a further decline of the bond price?
e. Does this exercise make you think about the debt situation of Western countries? (a few short sentences/ideas will be fine).
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2 – Forward Pricing
Suppose that your company has a floating rate USD loan outstanding with your bank whereby your company pay 3 months Libor +200 bps every quarter. The notional amount is USD 3 million. Now the CEO comes to you (you are the Treasurer). He is worried that short-term interest rates could go up over the next 2years. He urged you to call the bank to try to change the loan from floating to fixed rate but you are not happy with their pricing (they want a big “breakage fee” for cancelling the floating rate loan).
a. What hedge could you propose to your CEO instead?
b. How would you execute it? What exchange? What contracts? How many? What rates could you lock in?
– show your results in a table. Assume that interest payments on your company’s loan are at the end of each quarter (June, Sep, Dec, March etc)
3 – Forex-Hedging
You are running a business in Latvia where you produce and source your products. Your key clients are in Sweden. Now you are getting worried that the EUR might strengthen against SEK and that at some point you might have to raise prices in SEK which your customers would not be happy about. You will sell a minimum EUR 1.5 million of goods to Swedish customers in each of the next 3 years (to end of June 2016, to end of June 2017 and to end of June 2018. You would like protect your business from a potential decline in SEK vs EUR:
a. How can you hedge your currency exposure in general in this situation?
b. What Over-the-Counter products offered by your bank could you use to hedge the risk (Rough description is enough)?
c. How would you hedge using currency futures (is there a suitable futures contract traded? How many would you buy and sell? With what maturity?)
4 – Stock Option /Black Scholes Exercise
You will work with 2 companies’ stock prices in this exercise:
1. Pick two (2) large European companies in a EUR zone country of your choice that have liquidly traded shares on a major European stock exchange. (To avoid duplicity resp. complicity – your company names must contain both first letters from your first and last personal name). Collect the companies’ daily stock prices and calculate daily returns for the period since January 1, 2015 to now.
a. Put all data into an excel table (yahoo finance will help you).
2. Create a portfolio of the 2 shares where each company had roughly the same value at January 1, 2015, i.e. EUR 100’000 (total value of share portfolio at January 1, 2015 was correspondingly €200’000). You may assume that the companies’ stocks do not pay a dividend!
a. Calculate the portfolio’s development over time and put the figures into the spreadsheet
Answer the following questions:
– Price a call option on each stock and the portfolio as of today (June 14, 2015): For each option assume that the implied volatility (sigma σ) to price the option is the observed (historical volatility) you measured over the previous 5 months period. Create the requisite model.
▪ Maturity of both calls is 4 months (October 14, 2015)
▪ For the risk free, use Libor (from the table handed out in the course)
▪ Strike price of each option is At-the-Money (ATM) (closing price of stock on June 11 or 12)
A. What is the price of the call today (show your detailed Black Scholes calculations) – of stock 1, of stock 2 and of the portfolio?show the absolute price and as a percentage of last stock price
B. What can you say about the relationship of the individual prices of the call options on the stocks in comparison to the price of the call option on the portfolio?
C. Calculate the Delta of each option today and that of option of the portfolio? What does that mean to you in practice?
5 – Distribution of Stock and Currency Returns
Create a Histogram (diagram that shows frequency of occurrences) for each of the following data streams. To do this exercise in Excel, you may have to load the Analysis Tool pack in Excel first. You find under “Data” in Excel the function of “Data Analysis” – the Help function in excel will help you); There is a function “Histogram”. Choose an appropriate bin size:
– Use the data from previous exercise. For the two stocks and the returns of the stock portfolio, choose a “bin size” of 0.5% or smaller (0.25%). Create the histograms.
– Also look at the daily development of the currency pair US Dollar and Swiss Franc for the same period (Jan 1, 2015 to now). Pick an appropriate bin size. You may find the data in the research data base of the Federal Reserve Bank of St. Louis (US). They have a very good economic and financial market data base called FRED (something that may be helpful in other courses which is why I wanted to bring it to your attention J ) . http://research.stlouisfed.org/fred2/
A. Does each histogram approximately have the characteristics of a Normal Distribution?
B. What are the implications of using Black Scholes option pricing model if the stock returns (e.g. daily returns) are not approximately normally distributed?
C. How to derivative traders and option sellers adjust for the fact that stock returns (or returns on pretty much any other asset) is not exactly normally distributed?
D. What is the risk called for which there is a “Greek letter” that Option trades are most worried about? How can they hedge against this risk?
E. As you may note, the Swiss Franc appreciated sharply on January 15, 2015 due to the Swiss National Bank’s decision to end the costly intervention to prevent the Swiss Franc from appreciating against the EUR beyond 1.20 (As a matter of fact, they were practically coerced by the market). What is the implication of such developments on financial modeling in general? (such as for VaR models) etc.
6 – Q&A (Bonus Question)
Somebody made the argument that we live in an “asset rich – income poor economy”. Do you agree/disagree? What are the implications for you?
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