Module 6 - Fixed Income PDF

Module 6 - Fixed Income Bond Market Part 2 Part A. The Term Structure of Interest Rates This is a set of interest rates for a class of assets such as bonds, BABs, NCDs for a range of terms - The relationship between the interest rates of different financial instruments with different terms of time...

Module 6 - Fixed Income Bond Market Part 2 Part A. The Term Structure of Interest Rates This is a set of interest rates for a class of assets such as bonds, BABs, NCDs for a range of terms - The relationship between the interest rates of different financial instruments with different terms of time horizons. For example, we could examine the term structure of the BBSW by looking at its yield for securities with term of 30, 60, 90, 120, 150 and 180 days. A yield curve is a graph of the term structure of interest rates at a particular point in time. - Horizontal axis is time to maturity - Vertical is YTM rates - Each different plot is for the next longer term security - Plots interest rates against the maturity of debt instruments - It is upward sloping - The shorter term interest rates are lower than longer term interest rates which reflects the market expectation of things like market expectation and economic growth. - The level of long term bond yields reflect inflation rate expectations - The level of short term rates reflect monetary policy - Tightening monetary policy causes higher ST interest rates Term Structure is synonymous with Yield curve It’s mportant as it gives insight of expectation of market participants of future market conditions and monetary policy Term referring to time to maturity — Referring to debt securities as we’re talking about interest rates Yield curve shows yield to maturity for different securities of different terms. The impact of coupon paying bond calculations is that these will be outliers due to higher rates and therefore bonds are stripped form their coupon payments, which therefore lowers the yields, meaning they can be placed on the yield curve without relevant rates for risk free securities. Yield curve could be based on NCDs, BABs or Treasury Notes Government security yield curve w old sit below the bank securities yield curve due to decreased risk. Yield curve gives us indication of where rates could be in the future. Use yield curve to find expected forward rate in 5 years time. Yield Curve Shapes Inverse Yield Curve Features:Shorter interest rates are higher than longer term ones - Associated with an economic recession. - Inverted yield curve implies investors expect economic growth to slow down - They are seeking to lock in higher long term interest rates before they fall further. Flat Yield Curve Features: Generally similar rates regardless of security’s term - Not a common occurrence, happens for a short amount of time because we transitioning from normal to inverse or inverse to normal. - Happens when economy is transitioning from recession to growth or form growth to recession. - Monetary/interest rate/economy uncertainty can cause flat curve Normal Yield Curve - Shorter interest rates are lower than longer term ones (Most Common) Features: Slopes upward as shorter term rates are lower than longer rates (makes sense given TVM and risk, longer term = more risk) In reality, they are not as perfectly formed as a simple curve — — it goes up and down. If shapes are irregular like the inverse or flat yield curves, then we know something is happening in the economy that isn’t normal. Constructing Yield Curves 1) Yield curves are constructed from the yields on traded securities (rather than bank deposits) - We can’t use deposits are they are open in an individuals name which means they cant be traded or sold to someone else. 2) The securities need to have little or no credit and liquidity risk as we want to compare equally risk weighted securities. - If we include a high risk security, there will be an outlier in the yield curve. —> BABs and Treasury Bonds are used. 3) The yields need to be calculated on single payment instruments such as BABs and NCDs —> Bonds need to be stripped of their coupons - Use a method called boot strapping where we take the securities (bonds) strip them of their coupon payments and value them separately. - The bond is then valued individually without the coupons. Spot Interest Rates Spot interest rates are the current rate of interest, for a range of terms - Such as the yield on a trade of BABs, NCDs, zero-coupon bonds The term of the spot rate is given by the security’s term to maturity We can refer to the Spot Rates as orn ( 0=Starting date and n= ending date e.g. if the term is 5 years the subscript would be 5) Spot = Something trading in the market right now. E.g. the current share price of Qantas Provides a benchmark for which other investments can be compared and helps investors make informed decisions about their investments Forward Interest Rates Forward interest rates commences at a future date and extends for a specific term - E.g. an arrangements to bow or at an agreed rate for 90 days, starting in one month. - This would mean a forward rate shown as 1r4 with the 4 being in months Forward interest rates are implicit in spot yields - But actual forwards are discovered in the futures market. It is a rate that two parties can agree on for a future security based on prevailing market conditions Used to determine the value of of a forward rate agreement - A forward rate agreement or contract is an agreement between two parties to exchange an asset at a future date at a determined price. Forward rates are important as they enable investors and traders to hedge against future interest rate risk. Protected from a rise in interest rates in the future by locking in a price. Part B. Yield Curve Theories Yield curve theories attempt to explain the curve’s shape or slope 1) The Unbiased Expectation Hypothesis Hypothesises that expectations of future spot rates determine forward rates and so, decide the yield curve’s slope. According to this theory, forward rates are based on the market’s expected future rate movements without any added risk premium. - A normal yield curve results when the market expects spot rates will rise in the future. - An inverse yield curve results when the market expects spot rate to fall in the future. The hypothesis implies yield curves provide interest rate forecasts. The theory implies that investors are rational and have accessed to all relevant info and therefore the expected return on LT bonds should be equal to the average return on ST bonds over the same time period. It assumes borrowers and lenders are unbiased in the choice between securities with different terms - e.g. a two period investor is indifferent between a two period security or two successive one period securities The theory ignores the transaction costs and price risk associated with the second approach. The unbiased expectation hypothesis, interprets the shape of the yield curve as reflecting the market’s current expectations regarding the level of future spot rates. This means that yield curves provide us with the market’s interest rate forecast. The theory implies that; a) Normal yield curves are the result of market expectations of increasing spot rates. b) Inverse yield curves reveal the expectation that spot rates will be lower in future periods c) Flat yield curves indicate the expectation of interest rates remaining steady at their current level. 2) The Liquidity Premium Theory: (Only explained for normal yield curves) Argues that yield curves include price risk premium that: - Are higher for long term rates OR - May be expected to change During the GFC, the credit risk premium that applies to banks increased - showing the market do impose risk premiums that increase with term and that these can influence yield curves. This theory states that investors are compensated for a potential loss of liquidity that arises from holding a long term bond and therefore they are assigned to higher rates to generate higher returns. The liquidity premium theory says that the choice between investment strategies is biased by price risk. - Consider an investor with a six month investment horizon. The investor could invest in: a) A bond with 6 months to maturity, when the investor will receive the face value and final coupon with no price risk OR b) A bond with 10 years to maturity to be sold with 9.5 years to maturity for an unknown price. This theory is only relevant for normal yield curves Implication is the yield for longer term securities will include a risk premium to compensate investors for their price (i.e. liquidity) risk. Assessment of Yield Curve Theories In isolation, the liquidity premium theory does not explain non-normal yield curves Variations in short term rates are most likely due to the market anticipating future changes in the cash rate, consistent with the unbiased expectations approach We assume forward rates reflect the market’s expected future spot rates but, that these expectations will not always be correct. Part C. Hedging Interest Rate Risk Risks for Borrowers & Lenders Lenders and borrowers have the opposite risk exposures and so the two can be expected to trade with each other in derivate markets to hedge their exposures. Risk for Borrowers Chance of upside risk - Where rates turning out lower than expected Floating rate borrowers face risk of future spot rates being higher than expected. Negative slope as borrowers earn more with lower interest rates Risk Exposure of a Company that Plans to Issue Money Market Securities: - A plan to borrow money market securities has the risk of interest rates being higher than expected, as this will cause the proceeds from the issue to decrease. - This is represented by a downward sloping Pales Diagram curve. - If int rates are lower than expected (lower than the forward rate), the borrower would raise greater than expected proceeds - If int rates were higher, they would generate less returns. Pales diagram: (Risk hedge diagram) Risk for Lenders Floating rate lenders face risk of future spot rates being lower than expected (they earn less interest) Upside Risk - Where rates turn out to be higher than expected Positive slope in Pales Diagram as when rates increase, lenders earn a greater upside due to more returns from interest. Risk Exposure of a Planned Investment in 90 Day NCDs One Month From Now: - Planned investment in 90 Day NCD faces risk of a fall in interest rates prior to the investment - Upward sloping curves represents the risk exposure of a planned investment since it earns a lower return if the rate is lower than expected (below the forward rate) and benefits form a higher than expected rate (higher than the forward rate) Derivatives Derivatives are instruments (or contracts) whose value is linked to the value of another financial instrument, market variable or index. - They perform the risk transfer function. Interest rate derivatives can be used to hedge interest rate risk by transforming the spot interest rate at which funds are borrowed and lent into the forward rate. - They do not arrange the loan, borrowing takes place through banks or through the financial markets. A derivative’s value is derived form an underlying asset such as a share, bond, commodity, index, interest rate Used to manage risk and speculate market movement or hedge against potential losses Common types: options, futures, swaps and forwards contracts. Allows investors to take on different levels of risk exposure and to customer their investments to suit their needs. Derivatives and derivative contracts are complex and risky. Hedging with Derivatives The forward rate is established through the payment of a cash settlement When the derivative contract is agreed, neither party knows if they will pay the cash settlement or receive it because this depends on the future spot rate. —> When spot rates are higher than expected the borrower is compensated by being paid the cash settlement. —> When spot rates are lower than expected the lender is compensated by being paid the cash settlement. The market for derivatives comprises hedgers who are seeking to manage risk exposure. - and in some cases, speculators who seek to profit from accepting a risk exposure. The main interest rate derivatives are FRAs, interest rate futures, swaps and options The Outcomes of Hedging For a borrower: - A forward rate hedges the risk of higher than expected rates - But eliminates the chance of benefiting from a lower than expected rate For a lender: - A forward rate hedges the risk of lower than expected rates - But eliminates the chance of benefiting from a higher than expected rate. Interest rate Risk Exposures Banks, businesses and governments have interest rate exposures when they: 1 Plan to borrow or lend and/or 2 They borrow or invest at a floating rate Examples: - Businesses that borrow using a bill facility as rollover date may have changes in rate - Financial institutions when they borrow on a floating rate and lend on a fixed rate - Fund managers who rollover money market instrument For the borrower: if rates increase, then each price will be lower than expected resulting in higher than expected interest payments For the lender: the future return depends upon the market yield, which is unknown Both may prefer to ‘lock in’ forward rate rather than face uncertainty of future spot rates. Part D. Forward Rate Agreement An FRA is a contract with a bank that serves to establish a forward interest rate for a specified future date on a nominal principal for a set period. The FRA contract; - Has no upfront cost - Achieves the forward rate through the payment (+ or -) of a cash settlement calculated as the difference between a future spot rate and the agreed forward rate. Financial contract allowing two parties to fix an int rate on a future agreement Common, well established in market. Not traded on organised exchange but on OTC markets meaning they can be customised to meet specific needs of the parties involved. FRA Contracts We define FRA by its starting and finishing months. - E.g. a 1:4 FRA @ 5.00%, sets a rate of 5% for 3 months starting in one month. —> 1:4 with 1 being 1 month from today and 4 being the security maturing 4 months from today meaning the term is 3 months —> Company goes to bank and asks to agree on fixed forward rate through a FRA - A strip of FRAs (e.g. 1:4, 4:7, 7:10) hedges a series of exposures such as from a bill facility. FRAs use standard documentation that specify: a) Their Settlement date b) The term of the rate c) The amount of which the rate applies d) Whether it is a borrowing or lending rate e) The cash settlement equation — The equation used with discount securities —> Settlement = V agreed=[]’/ - V market (SCREENSHOT FORMULA) The FRA Market A primary, wholesale market conducted on an OTC basis The main dealers are the Big 4 and some international banks The main advantages of FRA are they: a) Meet each client’s requirements (made to measure) b) Are convenient to arrange because of standard documentation c) Pose low default risk (on the settlement payment) d) BUT they do not have a secondary market Both methods of calculating 2 yr rate or 1 yr rate and finding the second forward rate, should give you the same answer or FV. Calculating this is beneficial because we can calculate the expected forward rate. - can invest for - Calculations & add I spot Example to forward &yr rate & always rate I indicates forward = · rate - =.. & ⑤ 'b4 2 * Both methods of - %2 = 12 (n = g(n) ((n + (2x0 0 13 - 065) (12 -. -. 0 13 = 6 6. / - - 1) + -n - 1 x 1. 2nd forward. * 864) 1(8 864) Iniculating in 2 Spot Rates to 0 064. 6 6% Forward Rates 6 % 5 4%. 5% F2 F3 F ~ * Fo The Exact Method Itz : = n - 1 Mn = (n orn) ((n ~ = (2 12 5 802% =. = 7 21 %. x - 5 - 1) + 0 n 1) - 4) ((1)(5%)) -. 10 8% -5 %. = its + 5 8%. r 23 = = (3x6%) ((2)(5 4%)) -. 18% -10 8 %. = 7 2%. * ir2 Method The Approximate I steps1 beneficial as we can find the. forward rake. 2) Example you.. = finding the finding the rate will give the same answer of F 1). - calculating the 2 year rate or 1 year rate & then Irn N- = 12= H = = rate + F2 1(1 8 865)2 1(1 + 0 864) The Approximate Method The Exact Method year term lyr spot rate yr forward today (spl F always indicates spot full 2 can also invest a 283 expected 3) Example 3 : Forward Rates to spotrates 8 1% 7 6% 7%.. in * y - *Standard would be FVz (1 +,ig)3 - jog int but as 03 insistent we use individual spot rate) , The Exact Method org = (1 o rs)" + 1+ The Approximate Method (1 = v Ty = or s =. 2 = (Hore) orz - =.. 0+ 6)21 88))"3. ((1 87)(1 076)(1 38)]'s. - 1.. 7 566% r. (1 =. 87)(1 875). (11 87)(1 0763]"3, = - - 7 3% = non on 87)(1 376)(1 88) (( 07)(1 = ·. =. 7 567 %. * The approximate method is based on the premise that multiperiod spot rates are approximately the average of single period spot rates. Part D. Forward Rate Agreements Making an agreement today regarding a forward rate. Company would want o agree on a forward rate today as it’s unknown what the spot rate will be in 60 days and therefore hedges this risk. FRA Formula; 4) Example4 : FRAs))Hedging Settlements for With an FRA A & know * ① occurs at 49199331 - -$23886 - ② reffective -I = 49223217 6 6%. + as cash rate has decreased borrower will this means 423217a save positive-bank pay / borrower 50 mil agreed FRAStAUy negative-borrower pays = Basically confirming pay money to initial proceeds of the bill are found using lash setement equation settlement-mi) = that because rate , & *settlement straight away decrease the borrower will 1-25885)-1) money Therefore borrower Pays the bank + bank FRA rate 5) 5 Example is FRA entered Still 6 6%. (8 866 $35876 1 = + x. I reffective 50 mil 50 Mil settlement= t ( 869x95) 1+ 0. + 50000000 49163546 + 35876 6 6% S. 6) Example 6 settlement & I+ 0 = reffective J = - Example. 0275() $18256 Leasig20 30030 000 2 75. 7) - - 18256 1 + 0 825x). -(x % & settlement , 000 ess 120 = #+ 0 :. 0375/] $29842 = reffective 30000000 30000000 = 1 + 0. 0305 (128000000 -(x 118871535 + 29842 market P) = 128 800 008 3 75 %.