MARKET INPUTS Joint UNCTAD, IMF and World Bank MTDS Workshop Geneva, October 1-5, 2018
MARKET INTEREST RATES The cash flows as well as the cost and risk of a given debt management strategy will depend on the future path of interest (and exchange rates), which are unknown How to determine them? Assume constant rates Ask analysts to prepare forecasts and take an average Link to projections for policy rates, inflation, and GDP growth Use market information, perhaps even data from more developed markets
WHAT IS A YIELD CURVE? Yield curve is snapshot in time of yields showing the relationship between yield and maturity (should consist of fixed income securities with the same or similar risk profile) Family of yield curves Yield to maturity (redemption yield) Type Yield to maturity (Redemption Yield) Description Commonly encountered in markets Used in analysis and pricing activity Assumes constant rate of reinvestment Par yield Par yield = coupon rate Used in primary market to determine the required coupon for a new bond to be issued at par Determined from the spot yield curve by iteration Spot (Zero) Liquid zero-coupon (e.g. T-bills) Rare for longer dated instruments Can be derived from yield to maturity curve or par yield curve Term structure of interest rates No reinvestment risk, therefore ideal to use in relative value analysis Used in deriving implied forward rates Forward Spot yield is the geometric mean of the forward rates Plot of forward rates against term to maturity
WHAT DETERMINES THE SHAPE OF THE YIELD CURVE? Pure expectations theory At its simplest, yields on a long-term instrument should be equal to the geometric mean of the yield on a series of short-term instruments. Under this hypothesis, the most important determinant of long-term yields are expectations for the path of short-term interest rates. Nominal short-term interest rates are mainly determined by monetary policy, which in turn is driven by fundamental economic performance and inflation expectations Real rate (3%) Expected inflation (2%) Nominal yield (5%) Term premia - a bolt-on to pure expectations theory: investors require compensation for tying their money up for 10 years rather than reinvesting in short-term rates. Inflation risk premia the more volatile inflation is, the higher the yield premium to account for the uncertainty in future inflation. Credit risk premia lenders demand higher compensation to lend to riskier borrowers. Liquidity premia investors prefer instruments that can be easily traded in the size required without influencing the market price. The less liquid an asset, the higher the yield. Preferred habitat some investors demand bonds of a certain maturity for exogenous reasons e.g. pension scheme liability matching may depress yields at the long-end if demand is high relative to supply
BUILDING A YIELD CURVE Begin with foreign currency debt Build on mature market curves: any international bonds can be issued (priced) at a spread to benchmark bonds (e.g., a US 10-year Treasury) Determine likely credit premia to derive implied FX sovereign curve: May need to use peers to set plausible spreads Presumes that credit rating has been established For some countries access to market data is limited the domestic market for government securities is thin and short interest rates are not market determined Fixed exchange rate policy Macroeconomic projections can provide a reasonable alternative MoF, CB, IFIs or investment banks But still need assumptions about term structure
USE PEER DATA IF NO OWN DATA EXITS If no data exists... add a credit spread to US Treasuries (based on relevant peer data) 7 6 % US UTP $ Utopia ($) 5 4 3 2 1 CREDIT SPREAD US 0 1M 6M 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
SPREAD OF SOVEREIGN BONDS TO USD, (BASIS POINTS) Spread of Sovereign Bonds to US Treasury Bond (Basis points) 1000 800 Azerbaijan 2024 Belarus 2027 Mongolia 2022 Pakistan 2024 600 400 200 0 2014 2015 2016 2017 2018 Source: Bloomberg LP; and staff estimates and calculations.
YIELD CURVE IN DOMESTIC CURRENCY If interest rate parity is feasible, build on implied FX sovereign curve using inflation differential: Anticipated inflation differential is a proxy for anticipated currency appreciation/depreciation Consider other market specific factors: Liquidity premia will be important Inflation risk premia will be important (for longer dated instruments) monetary policy less credible than in baseline mature markets
If no data exists... assume projected inflation differential % 12 10 US Utopia (UTP) 8 6 4 2 INFLATION DIFFERENTIAL CREDIT SPREAD Utopia ($) US 0 1M 6M 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30
WHAT IF A MARKET CURVE EXISTS? Compare existing curve to that implied by inflation differential Difference? Explained by: o Liquidity and other risk premia o Domestic yield curve determined by idiosyncratic supply/demand May not extend sufficiently If one wishes to consider introducing longer tenors necessary to make assumptions about term premia or build on determined curve (e.g., by holding liquidity and other premia constant at last observed point)
FORWARD YIELD CURVE Are we done yet? Not quite. We now have the relevant yield curves for current period, but need yield curves for each year within the time horizon. What can we do? Can determine the market s expectations of future rates from current/spot yield curves using no arbitrage principle.
FORWARD INTEREST RATES A forward interest rate can be denoted f(t,τ,t) Where t = current time, τ = starting point of the forward contract, and T = maturity of the forward contract t=0 τ =1 T=2 Time f(t,τ,t) = f(0,1,2) For example: f(0,1, 2) represents: a contract today (t=0) to borrow money for one (T- τ = 2-1) year in one year time (τ =1)
GENERAL FORMULA FOR CALCULATING FORWARD INTEREST RATES 1 f ( t, τ, T ) = ( 1+ z( t, T )) ( 1+ z( t, τ )) z(t, T) T t τ t T τ 1 t τ T Time z(t, τ) Where z(t,t) = zero-coupon yield rates t = current time, τ = starting point of the forward contract, T = maturity of the forward contract f(t,τ,t)
IMPLIED FORWARD INTEREST RATES CAN BE DETERMINED FROM ZERO COUPON RATES z(0,2) 0 1 2 Time z(0,1) f(0,1,2) In an efficient market, the decision to invest 100 today for 2 years or invest 100 today for 1 year and then reinvest in 1 year, should make investors indifferent. 1 + zz 0,1 1 1 + ff 0,1,2 = 1 + zz 0,2 2 ff 0,1,2 = 1 + zz 0,2 2 1 + zz 0,1 1 1 1
EXAMPLE Assume: 1 year spot rate is = 0.4% and 2 year spot rate is = 1.0% What is the forward rate for 1 year rate in 1 year time? Expressed in terms of the formula s(0,1) = 0.4% s(0,2) = 1.0% What is f(0,1,2)? s(0,2) =1% 0 1 2 s(0,1)=0.4% f(0,1,2) =? Time
EXAMPLE s(0,2) =1% f ( t, τ, T ) = ( 1+ z( t, T )) ( 1+ z( t, τ )) T t τ t 1 T τ 1 0 1 2 Time s(0,1)=0.4% f(0,1,2) =? Solution: Investment at s(0,2) returns ((1 + ss 0,2 ) 2 = (1 + 0.01) 2 = 1.0201 Investment at s(0,1) returns ((1 + ss 0,1 ) 1 = (1 + 0.004) 1 = 1.004 Then: ff 0,1,2 = ((1+ss 0,2 )2 ((1+ss 0,1 ) 1 1-1 = (1+0.01)2 (1.01)2 1-1 = 1-1 = 1.6 (1+0.004) (1.004)
HOW TO USE YIELD CURVE TO PROJECT FORWARD RATES? 2 investment strategies: 2-year bond, invest in 2014 at 2% 1-year T bill, invest at 1% in 2014. Re-invest in new 1-year T bill in 2015, at unknown rate Which interest rate is needed on 1-year T bill in 2015 so that investor is indifferent between these two strategies? 2014 2% per year 2015 2% per year 2016 $100 1% per year?% per year $104.04 $100 $104.04
HOW TO USE YIELD CURVE TO PROJECT FORWARD RATES? 2014 2% per year 2015 2% per year 2016 $100 1% per year 3% per year!! $104.04 $100 $104.04 ff 0,1,2 = (1 + ss 0,2 2 (1 + ss 0,1 1 1 1 = 1 + 0.02 2 1 + 0.01 1 1 1 = 1.0404 1.01 1 = 3% f ( t, τ, T ) = ( 1+ z( t, T )) ( 1+ z( t, τ )) T t τ t 1 T τ 1
HOW TO USE YIELD CURVE TO PROJECT FORWARD RATES? Building Yield Curve 2 investment strategies: 2-year bond, invest in 2014 at 2% 1-year T bill, invest at 1% in 2014. Re-invest in new 1-year T bill in 2015, at unknown rate Yield 4% 3% 2% As of 2014 As of 2015 Which interest rate is needed on 1-year T bill in 2015 so that investor is indifferent between these two strategies? 1% 0% 1 2 Maturity (years) 2014 2% per year 2015 2% per year 2016 $100 1% per year 3% per year!! $104.04 $100 $104.04
MARKET INTERPRETATION (EXPECTATIONS) Upward-sloping Expectation is that future rates will be higher: Higher central bank policy rates (tighter policy) Higher inflation in future Anticipate stronger economic growth in future Downward-sloping Expectation that future rates will be lower Lower central bank policy rates Lower inflation in future Strongly inverted curves have historically preceded recessions Flat yield curve Expectation that future rates will remain the same
DERIVING FX DEVALUATION FROM INFLATION DIFFERENTIAL 2017 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 US Inflation Forecast (%) 2.11% 2.13% 2.61% 2.40% 2.21% 2.30% 2.30% 2.30% 2.30% 2.30% 2.30% Utopia Inflation Forecast (%) 8.84% 7.74% 7.24% 7.00% 7.17% 7.37% 7.37% 7.37% 7.37% 7.37% 7.37% (1+Inflation US) 1.021 1.021 1.026 1.024 1.022 1.023 1.023 1.023 1.023 1.023 1.023 (1+Inflation Utopia) 1.088 1.077 1.072 1.070 1.072 1.074 1.074 1.074 1.074 1.074 1.074 Expected annual depreciation (PPP) theory 6.596% 5.497% 4.509% 4.488% 4.850% 4.960% 4.960% 4.960% 4.960% 4.960% 4.960% Note: If the domestic country has higher inflation, we expect the domestic currency to depreciate against the foreign; positive percent change indicate depreciation. Future exchange rate: S 1 = S 0 * (1+ e) where e represents inflation differential S 1 = S 0 * [ (1+ I x ) ( 1 + I y ) ] Spot: S 0 (USD/UTP) 15.000 15.989 16.868 17.629 18.420 19.314 20.271 21.277 22.332 23.440 24.603 Future : S 1 (USD/UTP) 15.989 16.868 17.629 18.420 19.314 20.271 21.277 22.332 23.440 24.603 25.823 Memo: S 1 = S 0 * [ (1+ I x ) ( 1 + I y ) ] Where: X= Utopia and Y=US S 0 is the spot exchange rate measured as the price of a unit of foreign currency expressed in terms of the domestic currency (i.e., the amount of domestic currency required to purchase foreign currency). For example: 15 UTP per USD at end 2015. S 1 is the exchange rate in the next period and so on. I X is the expected annualized inflation rate for the domestic country I Y is the expected annualized inflation rate for the foreign country