_2 Yield Curve and Maturity Gap 2013 - Interest Rate Risk Measurement Repricing Model REFERENCES Hogan W et al 2004 Management of Financial Institutions

# _2 Yield Curve and Maturity Gap 2013 - Interest Rate Risk...

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Interest Rate Risk Measurement Repricing Model REFERENCES Hogan, W., et al., 2004. Management of Financial Institutions. Brisbane Wiley, Chapter 4. Lange, H. et al., 2013. Financial Institutions Management. (3 rd ed). Sydney: McGraw Hill, Chapter 5. 1.0 Introduction * This topic will consider the risk faced by banks as a result of changes in market interest rates. * Interest rate changes impact a bank’s net interest revenue (NIR) as its interest income and interest expenses change. This will be the focus of this week’s lectures. * Interest rate changes also impact the (market) value of a bank’s assets and its liabilities, and therefore its equity, which will be the focus of next week’s lectures. * To understand the impact of interest rate changes, it is first necessary to understand the relationship between interest rates of different maturities, forward rates, and expected future interest rates. Hence, the yield curve and associated calculations will be considered first. Subscribe to view the full document.

2 2.0 The Yield Curve * Yield Curve - Plot of yields against maturity - Relation is the term structure of interest rates - All rates must reflect similar default risk - Usually default-free government securities * Example: * Normal yield curve - Upward sloping - Long term rates generally higher than short-term rates * Inverted yield curve - Downward sloping Living yield curve: - yield-curve-7923/ 3 * In BUS244 Treasury Management, it was shown that the yield to maturity i 0,n of an n-period instrument was the geometric average of the expected short-term rates as follows: 1 ) 1 ( ) 1 ( ) 1 ( , 1 1 , 0 , 1 1 , 0 n t t n t n t t n t n n i i or i i This however only applies for ‘pure discount’ (zero coupon) securities, or to coupon bonds only in the special case where the yield curve is flat. * The yield to maturity of a bond was calculated as follows: n d n t t d t k FV k C Value Market ) 1 ( ) 1 ( 1 where: C t = Expected NCF to debt security holders (interest) in period t n = Maturity term (periods) FV = Face value paid on maturity k d = Required rate of return per period on the particular type of security Subscribe to view the full document.

4 That is, the yield to maturity was the internal rate of return of the bond - that rate which would discount the coupon and face value cash-flows to equal the market value of the bond. Implicitly, coupons are assumed to be re-invested at the IRR. * The yield to maturity (k d ) on the coupon bond is therefore not the same as the yield to maturity (i 0,n ) determined from the geometric average of short term rates because the implicit assumption of the IRR method that the coupons can be re-invested at k d is violated . It will only be the same in the special case where the yield curve is flat. That is, where: d n n d n n t t n t n n n d t t n t d n n k i k i i i k i k i i i i , 0 , 0 , 1 1 , 0 , 1 1 , 1 3 , 2 2 , 1 1 , 0 or that ) 1 ( ) 1 ( that follows it ) 1 ( ) 1 ( since but ) 1 ( ) 1 ( hence ... 5 * Where the bond is a zero coupon, (pure discount or Subscribe to view the full document. • Spring '17

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