1. UNCTAD, World Bank and IMF Workshop Geneva, February 06-10 2017
MARKET INPUTS
UNCTAD, World Bank and IMF Workshop
Geneva, February

2. 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

3. 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)
Type
Description
Yield to maturity
(Redemption Yield)
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
Family of yield curves
Family of yield curves
Definition of 'Yield Curve'
A line that plots the interest rates, at a set point in time, of bonds having equal credit quality, but differing maturity dates. The most frequently reported yield curve includes 1m, 3m, 6m, 1yr, 2yr, 3yr, 5yr, 7yr, 10yr, 20yr and 3yr debt. The US Treasury yield curve representing the yields at these maturities is used as a benchmark for other debt in the market, such as mortgage rates or bank lending rates. The curve is also used to predict changes in economic output and growth.  
'Yield Curve'
The shape of the yield curve is closely scrutinized because it helps to give an idea of future interest rate change and economic activity. There are three main types of yield curve shapes: normal, inverted and flat (or humped). A normal yield curve (pictured here) is one in which longer maturity bonds have a higher yield compared to shorter-term bonds due to the risks associated with time. An inverted yield curve is one in which the shorter-term yields are higher than the longer-term yields, which can be a sign of upcoming recession. A flat (or humped) yield curve is one in which the shorter- and longer-term yields are very close to each other, which is also a predictor of an economic transition. The slope of the yield curve is also seen as important: the greater the slope, the greater the gap between short- and long-term rates.
Yield to maturity (redemption yield)

4. 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
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
Real rate (3%)
Expected inflation (2%)
Nominal yield (5%)

5. 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

6. 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. PEERS’ SPREAD OF SOVEREIGN BONDS TO USD

8. 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
A theory in which the interest rate differential between two countries is equal to the differential between the forward exchange rate and the spot exchange rate. Interest rate parity plays an essential role in foreign exchange markets, connecting interest rates, spot exchange rates and foreign exchange rates.
The relationship can be seen when you follow the two methods an investor may take to convert foreign currency into U.S. dollars.
Option A would be to invest the foreign currency locally at the foreign risk-free rate for a specific time period. The investor would then simultaneously enter into a forward rate agreement to convert the proceeds from the investment into U.S. dollars, using a forward exchange rate, at the end of the investing period.
Option B would be to convert the foreign currency to U.S. dollars at the spot exchange rate, then invest the dollars for the same amount of time as in option A, at the local (U.S.) risk-free rate. When no arbitrage opportunities exist, the cash flows from both options are equal.
Definition of 'Liquidity Premium'
A premium that investors will demand when any given security can not be easily converted into cash, and converted at the fair market value. When the liquidity premium is high, then the asset is said to be illiquid, which will cause prices to fall, and interest rates to rise.
For example, assume an investor is looking at purchasing one of two corporate bonds, each with the same coupon payments, and time to maturity. Assuming one of these bonds is traded on a public exchange, while the other is not, the investor will not be willing to pay as much for the non-public bond. The difference in prices, and yields, the investor is willing to pay for each bond is called the liquidity premium.
Inflation can have a dampening effect on investment returns and can cut deeply into investment return value if there is no offset for the inflationary risk. If you have a portfolio, for example, that returns 9%, but the inflation rate is 3%, the true value of your returns has been cut by about 33%. Inflation-linked bonds, however, can help to offset - or hedge - that risk because they increase in value during inflationary periods. A bond or other type of debt whose coupon rate changes with market conditions (short-term interest rates). Also known as "floating-rate debt".
For example, a floater bond may have the coupon rate set at "T-bill rate plus 0.5%.
Definition of 'Covered Interest Rate Parity'
This term refers to a condition where the relationship between interest rates and the spot and forward currency values of two countries are in equilibrium. As a result, there are no interest rate arbitrage opportunities between those two currencies.
As an example, assume Country X's currency is trading at par with Country Z's currency, but the interest rate in Country X is 6% and the interest rate in country Z is 3%. All other things being equal, it would make good sense to borrow in the currency of Z, convert it in the spot market to currency X and invest the proceeds in Country X. However, in order to repay the loan in currency Z, one must enter into a forward contract to exchange the currency back from X to Z. Covered interest rate parity exists when the forward rate of converting X to Z eradicates all the profit from the transaction.

9. If no data exists... assume projected inflation differential

10. What if a market curve exists?
Compare existing curve to that implied by inflation differential
Difference? Explained by:
Liquidity and other risk premia
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)
Definition of 'Covered Interest Rate Parity'
This term refers to a condition where the relationship between interest rates and the spot and forward currency values of two countries are in equilibrium. As a result, there are no interest rate arbitrage opportunities between those two currencies.
As an example, assume Country X's currency is trading at par with Country Z's currency, but the interest rate in Country X is 6% and the interest rate in country Z is 3%. All other things being equal, it would make good sense to borrow in the currency of Z, convert it in the spot market to currency X and invest the proceeds in Country X. However, in order to repay the loan in currency Z, one must enter into a forward contract to exchange the currency back from X to Z. Covered interest rate parity exists when the forward rate of converting X to Z eradicates all the profit from the transaction.

11. Forward Yield Curve Are we done yet? What can we do?
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 11

12. Forward interest rates
A forward interest rate can be denoted f(t,τ,T)
Where t is the current time, τ is the starting point of the forward contract, and T is the maturity of the contract 1 2
Time
f(0,1,2)
For example, f(0,1, 2), represents a contract today to borrow money for one (2 minus 1) year in one year time (period) 12 12

13. General formula for calculating forward interest rates13 13

14. Implied forward interest rates can be determined from zero coupon rates
Time 1 2
z(0,1)
z(0,2)
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.
f(0,1,2) = [(1+z(0,2))2 / (1+z(0,1))1]1 – 1
(1+ f(0,1,2) )* (1+z(0,1))1=(1+z(0,2))2
Definition of 'Zero-Coupon Bond'
A debt security that doesn't pay interest (a coupon) but is traded at a deep discount, rendering profit at maturity when the bond is redeemed for its full face value. Also known as an "accrual bond". Investopedia explains 'Zero-Coupon Bond'
Some zero-coupon bonds are issued as such, while others are bonds that have been stripped of their coupons by a financial institution and then repackaged as zero-coupon bonds. Because they offer the entire payment at maturity, zero-coupon bonds tend to fluctuate in price much more than coupon bonds.

15. What is the forward rate for 1 year rate in 1 year time?
Example
Solution
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?
Invest at s(0,2), return (1.01)^2 =
Invest at s(0,1), return (1.004)
Then f(0,1,2) = [(1.01)^2/(1.004)] -1 = 1.6
Expressed in terms of the formula
Assume:
s(0,1) = 0.4% and s(0,2) = 1.0%
What is f(0,1,2)?

16. 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 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
$104.4
$100
1% per year
3% per year!!
$100
$104.4

17. 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

18. Deriving FX devaluation from inflation differential
Definition of 'Purchasing Power Parity - PPP'
An economic theory that estimates the amount of adjustment needed on the exchange rate between countries in order for the exchange to be equivalent to each currency's purchasing power. The relative version of PPP is calculated as: S1=P1/P2 Where: "S" represents exchange rate of currency 1 to currency 2  "P1" represents the cost of good "x" in currency 1 "P2" represents the cost of good "x" in currency 2
In other words, the exchange rate adjusts so that an identical good in two different countries has the same price when expressed in the same currency.  For example, a chocolate bar that sells for C$1.50 in a Canadian city should cost US$1.00 in a U.S. city when the exchange rate between Canada and the U.S. is 1.50 USD/CDN. (Both chocolate bars cost US$1.00.)