Ideas: Returns & Risk, Fixed Income- Finance & Investments- R Studio Assignment

Assignment Task :

Task: 1.

1. (Risk-Free Price Risk) When we say US Treasuries (USTs) are risk-free, we mean that their payoff is certain. (Well, as certain as can be for a USD-denominated investment.) However, you can lose money trading USTs since their prices change with interest rates. To get a handle on that capital gains risk, we will calculate some volatilities.

• We want to get daily yields for some USTs at four tenors (times to maturity): 3M, 2Y, 10Y, and 30Y. Since a 3M T-bill expires in three months, we obviously cannot use the same bill over a two-year period. Therefore, the Fed creates yield series called constant maturity treasuries (CMTs). CMT rates are averages of yields for instruments maturing near a certain amount of time. We use these to infer the yield for a certain maturity. Get daily yields over the past three years for those four instruments. The yields are quoted in percentage points; thus yields of “1.23” and “0.002” are yields of 1.23% and 0.002% (i.e. 0.2 basis points). What is the average yield for each of these instruments over the three years?
•  We cannot calculate daily log-returns for CMTs. Therefore, we must use an approximation. To do this requires two steps: First, compute the changes in yields. Then, multiply those changes by the following numbers: -0.25 (3M), -1.98 (2Y), -8.72 (10Y), and -19.20 (30Y).2 The result is a percent chance for the bond price, on the same scale as the bond yields. Find the average of these approximated log-returns for each of the four maturities.
• Using these approximated daily log-returns, calculate a standard deviation for each maturity. These are estimates of daily log-return volatilities. Scale them up to an annual basis(remembering that there are about 250 trading days/year).
• Again using the approximated daily log-returns, calculate a semi-deviation for each maturity. These are estimates of daily log-return semi-deviation. Scale them up to an annual basis (remembering that there are about 250 trading days/year).

2. (Short-term Credit and Price Risk) While we say US Treasuries (USTs) are risk-free, this is not true for money deposited in a bank: That bank can fail. Eurodollar futures can be used to hedge the rate paid for large US dollar deposits in a top-credit London bank. (That rate is called LIBOR, the London Interbank Offered Rate.) Eurodollar futures are some of the most actively traded instruments in the world. Because banks and finance firms often anticipate cash flows well into the future, Eurodollar futures are not just liquid for a few maturities but for many maturities. For this question, you should look at near Eurodollars (ED1) which are used to hedge three- month rate risk and Eurodollars about two-years out (ED24).

• Since Eurodollar futures trade at prices (not yields), we can easily calculate daily log- returns for them. Using these daily log-returns, calculate a standard deviation for each maturity. These are estimates of daily log-return volatilities. Scale them up to an annual basis (remembering that there are about 250 trading days/year). Report the scaled-up volatilities.
•  Again using the daily log-returns, calculate a semi-deviation for each maturity. These are estimates of daily log-return semi-deviation. Scale them up to an annual basis (remembering that there are about 250 trading days/year) and report the scaled semi deviations.
• Compare the volatilities of these Eurodollar contracts to the volatilities of similar-term CMTs. How different are the volatilities? Why would this be? (d) Now we will examine a credit spread. The TED spread is the amount that short-term Eurodollars (the “ED” in TED) yield over a similar-term US Treasury instrument (the “T” in TED). To compute what 3M Eurodollars are yielding, just subtract their price from 100. So if 3M Eurodollars are at 99.735, that implies a yield of 100?99.735 = 0.265 aka 0.265% or 26.5 basis points (bp). The TED spread is then found by subtracting the 3M CMT yield from this number. If the 3M CMT UST is yielding 0.03% (3 bp), then the TED spread is 23.5 bp. Calculate and report the historical average, volatility, and semi deviation for the TED spread.

3. (Equity Price Risk) Stocks are not risk-free: they may be rendered worthless (or nearly so) in bankruptcy; and, dividends may be reduced or suspended. All of these possibilities affect the risk of stocks. To get a handle on that risk and how it compares to price risk for USTs, we will calculate more volatilities. For these questions, use the ticker assigned to you. (For example, if my ticker were DAL its Quandl ticker would be YAHOO/DAL.)

1.  Get daily prices over the past three years for your stock, the S&P 500, and the Russell 2000.3 This means you will be working with three equity instruments. For your stock, make sure you get prices that are adjusted for dividends and splits; or, you may get dividends and splits and do the adjustments yourself. What is the average price of each of the equity instruments over the past three years?
2.  Calculate daily log-returns, differences in logs of daily prices, for all three equity instruments. Find the average log-return for each equity instrument.
3.  How do these average daily log-returns (when annualized) compare to average UST yields? Does this make sense? Why?
4.  Using the daily log-returns, calculate a standard deviation of log-returns for each equity instrument. These are estimates of daily volatility. Scale them up to an annual basis (remembering that there are about 250 trading days/year).
5.  Again using the daily log-returns, calculate a semi-deviation of log-returns for each equity instrument. These are estimates of daily semi-deviation. Scale them up to an annual basis (remembering that there are about 250 trading days/year).
6. How do the volatilities and semi-deviation compare between the equity instruments and USTs? Does this make sense? Why?

4. Save the data and, if you used R, the commands you used to do this homework. Print out your answers AND all the commands — and turn both in. Note that if you do not turn in your code, you will get no credit for this assignment. Also, if the code you turn in does not actually work, you will lose points. You will use the commands and data in Homework 2, so getting these points will make your life easier later.

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