Part 1:

You are required to collect the most recent bond market data, namely, yields to maturity, over the periods for which you have the data for both USA AND JAPAN.

(Your data must be from reliable sources, e.g., you should not collect the data from personal blogs. Also, it should not be from too generic sources, i.e., you should not collect data from Wikipedia).

Part 1A:

Collect the Yields to maturity and other relevant data, if any, for the maturities of 1, 2, 5, 10,

20, and 30 years. Present your data clearly and neatly in a properly formatted table.

Part 1B:

Consult the Appendix to this Assignment to gain a basic understanding of the Approximate Method for predicting future interest rates. Use the Approximate Method to calculate the discount rate ("DR") that the bond markets appear to consider appropriate over the following periods (see the Appendix):

- For 1-year

• -A veraged
• -A veraged
• -A veraged
• -A veraged
• -A veraged

over 1 - 2 years over 3 - 5 years over 6 - 10 years over 11 - 20 years over 21 - 30 years

Show all of your detailed workings for at least one country, i.e., either for the US or for the country of your own choosing, or both (to be included in the Appendix of your submission). Present your calculations clearly and neatly.

Part 2:

Use the reliable internet sources to collect the predicted rates of inflation for all the periods for which you have forecasted the Discount rates. Use your calculated Discount Rates and these inflation rates to predict the real rates of interests for those periods based on the following formula:

3

=1+ 1 1 +

For the future periods in which there are no predicted inflation rates, you can assume either that the last predicted inflation rate will stay constant for such periods or that the last real rate of interest as calculated will stay constant.BUT you are required to JUSTIFY your assumptions.

Show all your detailed workings, for at least one country, in this part of your Assignment. You can present these workings in an Appendix if necessary.

Part 3:

Use your results to compare thepredicted ratesbetween the USA and your selected country. Make sure that you use yourown economic analysisof your results or findings.

(For example, stating that one rate is higher than the other without any further comment on the reasons for it does not constitute economic analysis).

(If you use any other expert opinions from such sources as financial newspapers or statements by some central banks, make sure to quote the source properly).

Part 4:

Use your forecasting results in previous parts to make comments on the US market and the rates on TIPS (Treasury Inflation-Protected Securities).

Part 5:

Comment on how the YTMs of Treasury bonds have changed sinceApril 30th2019as below, eg. how does the market appear to have changed its predictions?

Year-bond US Cash 2.25% 3-month 2.31% 6-month 2.28% 12-month 2.10% 2-year 1.84% 5-year 1.85% 10-year 2.08% 20-year 2.61% 30-year 2.55%

Part 6:

US TIPS -

- - - -

0.28% 0.35% 0.42% 0.73%

Australia 1.50% - - 1.20% 1.11% 1.17% 1.48% 1.95% 3.15%

Japan Germany 0.10% 0.00% - - - - -0.15% -0.58% -0.19% -0.67% -0.21% -0.57% -0.10% -0.20% 0.29% 0.21% 0.45% 0.41%

UK 0.75%

-

- 0.62% 0.56% 0.61% 0.86% 1.33% 1.45%

Use the relevant theories of the term structure of interest rates to discuss how they affect your interpretation/results/findings.

4

Part 7:

In the light of your findings, comment on a Trump Tweet callingthe Fed "boneheads" and saying"... the Federal Reserve should get our interest rates down to zero, or less, and we should then start to refinance our debt. Interest cost could be brought way day while at the same time substantially lengthening the term...".

(Source:https://www.cnbc.com/2019/09/11/trump-says-fed-boneheads-should-cut- interest-rates-to-zero-or-less-us-should-refinance-debt.html)

Part 8:

Discuss how you see the implications of your findings for the equity markets.

5

APPENDIX - APPROXIMATE METHOD.

Example 1: Expected Interest Rates & Inflation Rates.

According to theexpectations hypothesis, a bond's yield to maturity (YTM), which represents investors' required rate of return on the bond, is directly related to expectations of inflation andprevailing interest rates. Thus, consider the following:

1. Expected Interest Rate: A Treasury bond with a face value of $100 and a coupon payment of 7.1% has one year to maturity. Thus, 1 year from now, the bond is scheduled to make a payment of $100 together with a final coupon payment of $100 * 0.071 = $7.1. If the bond is currently priced at $102.00, the YTM for the bond is

$102.00 =$107.11+

So, YTM = 0.05, or 5.0%. Therefore, we determine 5.0% as the prevailing 1-year interest rate on Treasury bonds. Since Treasury bonds can be considered effectively free from default risk, they provide a useful benchmark for interest rates. For instance, if inflation is running at, say, 2.4% per annum, we might deduce that bondholders require a risk-freerealrate of interest per annum of approximately 2.6% per annum ( 0.05 - 0.024), or more precisely,

Real rate of interest =1 + nominal interest rate 1 1 + inflation rate

=).*+ 1=1.02541=0.0254=2.54%).*,-

2. Expected Inflation Rate: Now suppose that at the same time, a 2-year Treasury bond with a face value of $100 is scheduled to make a coupon payment of 7.1% both 1 year and 2 years from now, and that it is currently priced at $102.99. To determine bond investors' required rate of return on this bond in Year 2, that is,YTM12, we solve the following equation:

$102.99 =$7.1+$107.1, 1 + )(1 + ))(1 + ),)

whereYTM1is the YTM in Year 1 (determined for one-year Treasury bonds as above = 5.0%) andYTM12is the YTM in Year 2. Hence,

$102.99 =$7.1+$107.1, 1 + 0.05 (1 + 0.05)(1 + ),)

6

which yieldsYTM12(in Year 2) = 0.06 (6.0%).

Therefore, it appears that the market anticipates an annual interest rate of 6.0% for Treasury bonds in Year 2, and accordingly, if we believe that bond investors will continue to require arealrate of interest on Treasury bonds of 2.54% over 2 years, the bond allows us to predict the investors' anticipated inflation rate, denoted asinflation rate2, for Year 2, as follows:

Real rate of interest,=1 + nominal interest rate,1 + inflation rate,

0.0254=1.06 1 1 + inflation rate,

1

So,inflation rate2(the anticipated inflation rate in Year 2) is

,=).*61 = 0.0337 = 3.37%

)7*.*,+-

Example 2: Forecasting Future Rates

Suppose that a Treasury bond with a face value of $100 and a coupon rate of 5.2% has 1 year to maturity (i.e., a "1-yearbond"). Thus, one year from now, the bond is scheduled to make a payment of $100 together with a final coupon payment of $100 * 0.052 = $5.2. If the bond is currently priced at $100.19, the yield to maturity for the bond over the coming 1-year period (YTM1) is

$109.19 =$105.21+)

which yieldsYTM1=$)*+., 1= 0.050, or 5.0%. This is the discount rate,DR1, that the$)**.)9

market considers appropriate over the coming 1-year period.

Now suppose that a Treasury bond with a face value of $100 and a coupon rate of 7.1% has 2 years to maturity (i.e., a "2-yearbond"). Thus, one year from now, the bond is scheduled to make a payment of $100 * 0.071 = $7.1, and 2 years from now, it will make a payment of $100 together with a final coupon payment of $7.1. If the bond is currently priced at $102.99, we can find the yield to maturity for the 2-year bond (YTM2) by solving the following equation:

7

$102.99 =$7.1+$107.1

1 + ,(1 + ,)(1 + ,)

Therefore,YTM2= 5.48%.

The question we now ask is:What is the discount rate, DR2, that the market appears to consider appropriate for the 2nd year?Note that it isnot5.48%, because this is the discount rateaveragedover the 2 years (and recall that the appropriate discount rate is 5.0% for the 1st year). In fact, to solve for the discount rate that the market is imposing in the 2nd year,DR2, we need to solve:

$102.99 =$7.1+$107.1

1 + )(1 + ))(1 + :;<)

whereYTM1is the YTM in Year 1 (determined for 1-year Treasury bonds as above = 5.0%) andDR2is the appropriate discount rate for Year 2 (YTM12). Therefore,

$102.99 =$7.1+$107.1

1 + 0.05 (1 + 0.05)(1 + :;<)

which yieldsDR2(in Year 2) = 0.060 (6.0%).Approximate approach

Instead of using the above equation to determine theDR2value in Year 2, we can approximateDR2by applying the following simple relation:

(1+DR1)(1+DR2) = (1+YTM2)2

(YTM2is the YTM for a 2-year bond), for which we haveDR1= 0.05 andYTM2= 0.0548, so that:

(1.05)(1+DR2) = (1.0548)2

Note: You can solve for YTMs using theIRRfunction in Excel. Alternatively, you can set up your Excel spreadsheet for the valuation of the bond as the fundamental equation above and gradually adjust the inputYTM2until you get the valuation to equal $102.99; this can be done easily using the Excel "Goal Seek" or "Excel Solver".

8

which yields the approximate value ofDR2= (1.0548)2/(1.05) - 1 = 0.0596 (5.96%), as compared withDR2= 0.060 (6.0%) as computed previously. Thus, the approximation appears sufficient.

Suppose now that a Treasury bond with a face value of $100 and a coupon rate of 5.0% has 5 years to maturity. Thus, one year from now, the bond is scheduled to make a payment of $100 * 0.05 = $5.0, and thereafter, until 5 years from now, make a payment of $100 together with a final coupon payment of $5.0. If the bond is currently priced at $91.80, we can solve for the yield to maturity for a 5-year bond (YTM5) using the following equation:

$91.80 =$5.0+$5.0+$5.0+$5.0+$105.0 1++(1++),(1++)>(1++)-(1++)+

which yieldsYTM5= 7.0%.

We now ask:What is the discount rate, DR3/5,that the market appears to consider

appropriate for years 3 to 5?To answer this question, we solve the following equation:

$91.80=$+.*+$+.*)7?@A()7?@A..?@B)

+$+.*+$+.*+()7?@A)()7?@B)()7?@C/E)A()7?@A)()7?@B..?@C/E)B

$)*+.* ()7?@A)()7?@B)()7?@C/E)C

whereDR1= 5.0% andDR2= 6.0%, so that:

$91.80 =$5.0+ 1.05

$5.0 (1.05)(1.06)

+

$5.0 (1.05)(1.06)(1 + F>/+))

+$5.0 (1.05)(1.06)(1 + F>/+),

+

$105.0 (1.05)(1.06)(1 + F>/+)>

which yieldsDR3/5= 8.16% .

Approximate approach

Note that rather than use the above method to determine theDR3/5value for Year 3 through Year 5, we can approximate it by using the following relation:

(1+DR1) (1+DR2) (1+DR3/5)3= (1+YTM5)5

for which we haveDR1= 0.05,DR2= 0.06 andYTM5= 0.07, so that:9

(1.05) (1.06) (1+DR3/5)3= (1.07)5

yieldingDR3/5= [(1.07)5/[(1.05)(1.06)]]1/3- 1 = 0.080 (8.0%), which compares withDR3/5=

0.0816 (8.16%) calculated earlier.

Nominal rates, inflation, and real rates

As Treasury bonds are regarded as effectively free from default risk, they provide a useful benchmark for interest rates. For example, if we predict that inflation will be running at, say, 6.0% per annum over the next 3, 4, and 5 years ahead, we can deduce that bondholders require a risk-freerealrate of interest of approximatelyDR3/5as calculated aboveminusthe inflation rate = 8.16% - 6.0% = 2.16% per annum. More precisely, we would deduce that bond investors anticipate a risk-free real rate of interest per annnum for 3, 4 and 5 years forward as

Real rate of interest =1 + nominal interest rate 1 1 + inflation rate

=).*G)6 1=1.02-1=0.020,or2.0%.).*6

Alternatively, if we considered that investors will have a required real rate of return on Treasury bonds equal to, say, 2.5%, we would deduce the market's prediction for inflation in years 3 -

).*G)6

5as).*,+-1=5.5%.

j