Summary

Term Structure of Interest Rates (Fixed Income Securities - Chapter 15) Summary

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Course
Finance IIB (FTX3045S)

Institution
University Of Cape Town (UCT)

Detailed and well summarised study notes of the "Fixed Income Securities - Term Structure of Interest Rates" section taught in Finance IIB at UCT (FTX3045S).

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Uploaded on February 21, 2023
Number of pages 15
Written in 2022/2023
Type Summary

finance iib
fixed income securities
study notes
term struture of interest rates
uct
summary

Institution
University of Cape Town (UCT)
Course
Finance IIB (FTX3045S)

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Fixed Income Securities Summaries

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1. Summary - Summary of "bond prices and yields" (fixed income securities - chapter 14)
2. Summary - Term structure of interest rates (fixed income securities - chapter 15) summary
3. Summary - Managing bond portfolios (fixed income securities - chapter 16) summary
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FTX3045S Summaries (all)

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9 items

1. Summary - Options markets summary (derivatives - part 1)
2. Summary - Options valuations (derivatives - part 2) summary
3. Summary - Futures markets (derivatives - part 3) summary
4. Summary - Futures and risk management (derivatives - part 4)
5. Summary - Summary of "bond prices and yields" (fixed income securities - chapter 14)
6. Summary - Term structure of interest rates (fixed income securities - chapter 15) summary
7. Summary - Managing bond portfolios (fixed income securities - chapter 16) summary
8. Summary - International finance - part 1 summary
9. Summary - International finance - part 2 summary
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FIXED INCOME SECURITIES – TERM STRUCTURE OF INTEREST RATES
(CH 15)

WHAT IS THE TSI?

TSI → relationship between the yields to maturity and term to maturity of a sample of
similar bonds.

Similar bonds
- should have similar characteristics → pure relationship
- must be similar → risk, liquidity, tax rates, coupon rates, credit quality
- doesn’t need to be similar → time to maturity

Shows how bond yields change with time to maturity
- time factor = time premium/time spread/price of time

Importance of the TSI

Used to extract spot rates which are applied in:
- pricing bonds
- extracting forward rates
▪ predict future interest rates & use them to formulate active bond strategies
- predicating future economic activity
- making investment decisions
- other uses (i.e. estimating inflation, monetary policies)

TSI ON A YIELD CURVE

Note:
- shape of curve changes with changes in interest rates
- yields generally move together

, - shape of curve is NB to investors & economists

Flat yield curve → investors want the same return for all instruments.

Upward-sloping yield curve → investors want higher return for long-term instruments &
lower return for short-term instruments.

Downward-sloping yield curve → investors want a higher return for short-term instruments
and a lower-return for long-term instruments.

Hump-shaped yield curve → investors want a lower return for short & long-term
instruments and a higher return for medium-term instruments.

Example 1:
You are given the following hypothetical term structure of interest rates based on zero
coupon treasury bonds each with a face value of R1 000.

Term to maturity (years) Yield Price (R)
1 5% 952.38
2 6% 890
3 7% 916.30
4 8% 735.03

- this is a pure curve, made of ZCB bonds, issued by the government
- the YTM for ZCBs are called spot rates
▪ TSI or spot rate curve or the pure curve

DERIVING SPOT RATES

DIRECT OBSERVATION METHOD

- works if given a pure yield curve, made of stripped treasury zero-coupon bonds
- YTM of a ZCB is the spot rate
- observe bond yields in the TSI → those are your spot rates

If given the prices & face values of ZCBs, use the following formula to calculate the spot
rate:

𝐹𝑉
𝑃𝐵 =
(1 + 𝑟)𝑛

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