The Structure of Interest Rates: Linkages Between Asset Yields

- See: Mishkin and Serletis, Ch. 6 and Ch. 18 Appendix pp. 486-489.

- Concern: the inter-relatedness of asset markets for the structure of interest rates.

- Why are financial markets interrelated?

- A major reason: borrowers and lenders view alternative assets as substitutes

- alternative ways of raising (borrowing) funds;

- alternative ways of saving (lending) funds.

- if the yield on an asset is high compared to yields on substitute assets:

- lending flows into the asset (demand shifts right): this lowers the yield.

- borrowers seek to borrow in cheaper ways (supply shifts left): this also drives the yield down.

- the yield on the asset (and its price) falls back into line with other yields as a result of these shifts.

- key point: flows of lending and borrowing between markets link yields.

1

- Last set of notes: Supply and demand model of an asset market

- positions of the demand (lender) and supply (borrower) curves for specific assets depend on yields of other assets.

- this builds in interdependence: a change in one market spills into other markets.

- Equilibrium interest rates (yields) will be equal if the assets are ‘perfect substitutes’

- If ‘imperfect substitutes’ equilibrium yields will differ by an amount sufficient to compensate for the differences between the assets.

- Linkages to be examined: all cases of imperfect substitutes

- Term structure theory (between assets with different terms)

- International interest rate linkages (between assets from different countries)

- Risk premia (relation between assets of different riskiness)

2

Term Structure of Interest Rates

Term structure: how do yields vary by term to maturity (‘other things equal’).

Yield curve:Shows the relationship between the term to maturity and the yield on

otherwise similar assets.

- Focus when measuring term structure is usually on government debt

- Why government debt?

- yields by term are likely to be purely “term effects”

- long- and short-term assets: similar risk (same risk-free issuer)

- good secondary market for government debt (similar liquidity across assets)

- so: differences in yields by term are likely to reflect only term structure.

- The term structure arguments are valid for any financial assets that differ by term to maturity.

- but if the assets differ in characteristics other than term it is harder to isolate the pure term structure effect.

3

- Yields curve shapes? (interest rate in % on vertical axis, term on horizontal)

3 mth 6 mth 1 yr 2 yr 3 yr 5 yr 7 yr 10 yr Long0.00

2.00

4.00

6.00

8.00

10.00

12.00

14.00

16.00

Yield curve examples

1990/061988/092006/102004/062013/01

3 mth 6 mth 1 yr 2 yr 3 yr 5 yr 7 yr 10 yr Long3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

11.00

12.00

13.00

More Canadian Yields Curves

1990/091988/072000/052006/10

4

Explanations of term structure

- We will look at three related theories:- Expectations theory- Liquidity Preference (extension of Expectations Theory)- Preferred Habitat (extension of Expectations Theory)

Expectations Theory

- Key Assumption: many lenders regard short-term and long-term debt as perfect substitutes (other things equal).

- Consequence for asset market equilibrium?

- Over the same lending period a sequence of shorter-term assets must provide the same yield as longer-term assets

- Look at this with a ‘zero coupon’ bond like a T-Bill (no coupon payment just a single payment, the argument can be extended to the more general case but is messier)

- Notation: R1, R2, … RN yields now on a 1-yr , 2-yr, … N-yr bond.

E11 is the yield on a 1-yr bond issued one year from now.

E12 is the yield on a 1-yr bond issued two years from now.

EMP would be the yield on a M-year bond issued P-years from now.

5

- Say the lender wants to save funds for two years (two year lending period):

Option 1: hold one two-year bondYield = R2 (NOTE: yield of 5%, R2=.05)

Invest $1 now, to get :

(1+R2)(1+R2) = (1+R2)2 in two years.

Option 2: hold two one year bonds sequentially:

Yield on first bond (matures in 1 yr): R1

Expected yield on second bond: E11

(E11 = yield on 1 yr. bond issued one year from now)

So invest $1 now to get:(1+R1)(1+E11) in two years time.

- Lender will be indifferent between the two options if:

(1+R2)2 = (1+R1)(1+E11) this must hold in equilibrium.

e.g., say (1+R2)2 < (1+R1)(1+E11)

- lenders buy one-year bonds, avoid two-year bonds- so R1 falls and R2 rises until equality holds (Supply-Demand!)

If instead : (1+R2)2 > (1+R1)(1+E11)

- lenders buy two-year bonds and avoid one-year bonds- so R2 falls and R1 rises until equality is established.

(Demand shifts between markets for 1-yr. and 2-yr. bonds drive the result)

6

- Generally: for an N-year lending period.

Option 1:

- Hold one N-year bond (average annual yield of RN) for N-years:

In N-yrs. $1 invested now pays (1+RN)N

Option 2:

- Hold n one-year bonds sequentially with:

- yield of R1 for the first bond and

- yield E1J for the 1 yr. bond issued J years from now.

One dollar invested now pays:

(1+R1)(1+E11)(1+E12)...(1+E1N-1) in N years (note there are N terms in

the expression)- Equilibrium:

(1+RN)N = (1+R1)(1+E11)(1+E12)...(1+E1N-1)

- then lenders are indifferent between the options

(no shifts of lending between the two options – shifts would change RN and R1)

7

- Similar reasoning links yields and expected yields of any combination of different-term assets held for the same time period

e.g. Say five years is the period lending occurs over:

- Some options: one 5-year bond; five one-year bonds; one 3-yr. bond, then one 2-yr. bond etc.

- You can write down an equilibrium condition for each pair of options, i.e. they should all pay the same in equilibrium.

(1+R5)5 = (1+R1)(1+E11)(1+E12)(1+E13)(1+E14) = (1+R3)3(1+E23)2

- Similar conditions for other lending periods.

- End result? A set of equations linking yields across the term structure.

8

- A convenient approximation to the equilibrium condition?

Yield on long-term = average of the yields on short-term assets

RN=R1+E11+E12+…+E1N−1

N

(Aside: where does this come from? take logarithms of:

(1+RN)N = (1+R1)(1+E11)(1+E12)...(1+E1N-1)

N∙ln(1+RN) = ln(1+R1) + ln(1+E11) + ln(1+E12)+…+ + ln(1+E1N-1)

and note that: log(1+i) i for small i so: ln(1+RN) RN etc.)

9

Some Implications of the Pure Expectations theory?

(1) Expectations of future yields determine the shape of the yield curve:

- Flat: expect stable future short-term yields

- Upward slope: future short-term yields will be higher than current yield.

- Downward slope: future short-term yields will be lower than the current yield.

i.e., consider R1 vs. R2:

(1+R2)2 = (1+R1)(1+E11)

R1=E11 then R1=R2

R1>E11 then R1>R2

R1<E11 then R1<R2

10

- More complicated yield curve shapes? Also reflect the pattern of expected future rates.

- Consider rate on R3 vs R2. Can write an equilibrium condition:

(1+R3)3 = (1+R2)2 (1+E12)

Then: R3=R2 if R2=E12 (flat curve between 2 and 3 yrs)

R3>R2 if R2<E12 (rising curve between 2 and 3 yrs)

R3<R2 if R2>E12 (falling curve between 2 and 3 yrs)

- So between 1 yr and 2 yrs yield curve shape reflects R1 vs. E11 and between 2 yrs and 3 yrs it reflects R2 vs. E12

- Odd shapes are possible with the right pattern of expected yields:

- Say R1<E11 so R2>R1 and R2>E12 so R3<R2. The yield curve slopes up then down! (plot this)

e.g. R1=.02, E11=.04 (implies R2=.03)then if E12=.02 have R3=.0267

- Say R1>E11 so R2<R1 and R2<E12 so R3>R2. The yield curve slopes down then up! (plot this)

e.g. R1=.02, E11=.01 (implies R2=.015)then if E12=.03 have R3=.02

(Note for a 3-yr. Period: (1+R3)3 = (1+R1)(1+E11)(1+E12) also holds)

11

(2) Yields on bonds of different terms to maturity will move together (given expected future yields)

(1+R2)2 = (1+R1)(1+E11)

(1+R3)3 = (1+R1)(1+E11)(1+E12)

If R1 rises (given expected yields) R2 and R3 must rise.

If R3 falls, (given expected yields) R1 and R2 must fall.

- The effect of a change in R1 is stronger if current short-term and expected short-term yields move together

e.g. if rise in R1 is typically associated with rises in the E1’s.

- An implication for monetary policy?

- Monetary policy typically targets short-term interest rates e.g. R1.

- Effect on RN will be weak unless expected yields change in the same direction as R1.

- Central banks can have greater effects on long-term interest rates if they can also affect expected future interest rates.

e.g. announce the likely path of future rates; ‘forward guidance’

Bank of Canada’s October Monetary Policy Report hints that it is moving towards a 3% overnight rate: are they trying to influence expected future yields?

12

(3) Given expectations, yields on short-term assets will be more volatile than long-term yields:

(1+RN)N = (1+R1)(1+E11)(1+E12)...(1+E1N-1)

- a change in RN is magnified by its being to the power of N.

- a large change in R1 is needed to balance it if expected yields are stable:

e.g., say that have an equilibrium:

R1 = .05 , R2 = .05 and R3 =.05 with E11 = .05 , E12 = .05

(1+R2)2 = (1+R1)(1+E11) = 1.1025

(1+R3)3 = (1+ R1)(1+E12)(1+E13) = 1.157625

- Say that R1 doubles to .10. Then if the equations above are to still hold:

R2 = .0747 (7.47%) R3 = .0664 (6.64%) i.e. much less than double.

- Doubling of R3 to .10 (expectations constant at .05) would raise R1 to .2073 for equilibrium.

13

What determines expectations of future short-term yields (E1J) ?

- Generally: anything which affects the position of future borrower (supply) and lender (demand) curves.

- Possible distinction: real and nominal rates

(a) Anything which changes the “expected real interest rate” or expected real yield.

e.g., expected future business conditions demographics (lifecycle theory of saving)business cycles, changes in risk & liquidityexpected monetary policy

- post-2009: did low post-crisis long-term yields in US reflect pessimism about economic recovery? (Paul Krugman)

- Oct. 2018 to Aug. 2019: 10 yr. yields falls by 1.36%, 1 yr. yield falls only 0.6% -- did this reflect pessimism about future growth?

Beliefs about monetary policy?

(b) Expected Inflation:

- determines the difference between the real and nominal yield.

- works through the Fisher effect.

- often discussed as if it is a key determinant of future yields.

- could current increases in long-term yields mean higher inflation expectations?

- Expectations theory suggests that the observed term structure can be used to identify current lender expectations (yields).

e.g. R1 > R2 implies that E11 > R1 : short-term (one-year are expected to rise)

i.e., the term structure can be used as a way of forecasting future rates.

14

15

Liquidity Preference, Risk and Term Structure: an Extension of Expectations Theory

- Long and short-term bonds are not perfect substitutes.

- Liquidity preference assumes there may be preference for short-term assets.

- Longer term bonds may be regarded as riskier. Why?

- More exposed to inflation risk (greater uncertainty regarding future inflation when time horizons are long).

- For those with uncertain (or short) holding times:

- “Thin” long term markets add to uncertainty of resale prices.

- Changes in interest rates affect resale price (interest rate risk).

- These problems are likely more sever the longer term to maturity.

- A premium on long-term bonds may be required if lenders think this way.

- So when:

(1+RN)N = (1+R1)(1+E11)(1+E12)...(1+E1N-1)

- the typical lender may prefer the sequence of one period bonds:

- so: RN will rise, R1 will fall until lenders are indifferent between the two options:

until a liquidity premium is paid.

- Equilibrium:

(1+RN-LPN)N = (1+R1)(1+E11)(1+E12)...(1+E1N-1)

LPN = liquidity premium on the n-period bond (text calls this lN).

16

- This premium will likely be higher the longer the term to maturity (text Fig 6-4)

- On its own, liquidity preference would lead to an upward sloping yield curve.

e.g., if yields were expected to be stable in the future

- Expectations hypothesis: predicts a flat yield curve

- Liquidity preference: predicts an upward slope.

- The most common shape of yield curve is upward sloping.

- an advantage of the liquidity premium view.

17

Preferred Habitat theory

- Some lenders prefer long and others prefer short term bonds (given same yield)

- Prefer short term: liquidity preference problem

- Prefer long term: concern about uncertainty of future short-term yields (if intend to lend long)

- Consequence? (new prediction)

- the relative supply of long and short term assets will affect the shape of the yield curve.

- relative to distribution of lender preferences

e.g., say half of lenders prefer short and half prefer long lending:

- If 1/4 of bonds are short term and 3/4 of bonds are long term:

- some lenders with preference for short term bonds will hold long term bonds.

- premium will be paid on long term bonds to attract lenders

- yield curve tends to slope upward.

- If 3/4 of bonds are short term and 1/4 of bonds are long term:

some lenders with preference for long term bonds will hold short term bonds.

- premium will be paid on short term bonds to attract lenders

- yield curve tends to slope downward.

18

Evidence on Term Structure Theories?

- Pure expectations:- yields on bonds of different terms do seem to move

together as the theory predicts

- greater volatility of short term rates seems consistent with the theory

- expectations determine the yield curve shape

- expectations are difficult to measure so hard to test this.

1936/011944/031952/051960/071968/091976/111985/011993/032001/052009/070

5

10

15

20

25

Government of Canada: 3 mth vs. Long-term, 1936-2014

Long-term (10+)T-Bill 3mth

%

19

2-Jun-82

2-Jul-8

3

2-Aug-84

2-Sep-85

2-Oct-

86

2-Nov-8

7

2-Dec-8

8

2-Jan-90

2-Feb-91

2-Mar-9

2

2-Apr-9

3

2-May-9

4

2-Jun-95

2-Jul-9

6

2-Aug-97

2-Sep-98

2-Oct-

99

2-Nov-0

0

2-Dec-0

1

2-Jan-03

2-Feb-04

2-Mar-0

5

2-Apr-0

6

2-May-0

7

2-Jun-08

2-Jul-0

9

2-Aug-10

2-Sep-11

2-Oct-

12

2-Nov-1

3

2-Dec-1

4

2-Jan-16

2-Feb-17

2-Mar-1

80

2

4

6

8

10

12

14

16

18

Government of Canada Bond Yields: 2 yr, 5-yr, 10-yr maturities 1987-2018

2 year 5 year 10 year

- Liquidity preference

- advantage: it suggests a bias in favor of upward sloping yield curves. This is the most common shape.

(see diagrams above; only 9.5% of the weeks since early 1982 have had the long-term bond rate lower than the 3-mth T-Bill rate.

- Preferred Habitat

- suggests that a bias toward upward sloping yield curves might be due to greater supply of long-term debt than lenders with preferences for long-term debt.

- unique prediction: relative supplies of assets of different terms will affect yield curve shape

- empirical studies divided on this prediction.

20

Exchange Rates and International Yield Differentials

- If similar domestic and foreign financial assets are viewed as good substitutes then substitution should link yields on domestic and foreign assets.

- Small open economy model of the Canadian financial markets: an extreme case

- Canada too small to affect world interest rates (big changes in Canada barely budge world supply and demand curves).

- Large flows of lending and borrowing between Canadian and world financial markets should keep Canadian yields tied to world yields.

e.g. Say Canadian yield higher than world rate on similar assets.- Foreign lenders switch to Canadian asset;

- Canadian borrowers borrow abroad.

- Rise in lending (asset demand), fall in borrowing (asset demand) in Canada lowers Canadian interest rate to world level.

21

(What happens if at the start iC < iworld and Canada is integrated with the World? Try drawing this)

- This suggests that Canadian yields would have to equal foreign yields in Equilibrium on similar assets.

- Evidence? - Canadian yields do tend to move with yields on similar US

assets.

- but yields are seldom the same: at times divergence is large similar assets.

- What’s missing? - Exchange rates are a possible candidate.

(other possibilities? risk or liquidity differences)

1962/01 1967/11 1973/09 1979/07 1985/05 1991/03 1997/01 2002/11 2008/090

5

10

15

20

25

Canada and US 3-mth T-Bill Yields 1962-2014

Cdn T-billUS T-bill

%

22

1982/061986/061990/061994/061998/062002/062006/062010/060

2

4

6

8

10

12

14

16

18

Canada vs US 5-yr Government Bond Yields

US 5 yrCdn 5yr

%

1982/06 1986/07 1990/08 1994/09 1998/10 2002/11 2006/12 2011/010

2

4

6

8

10

12

14

16

18

Canada and US 10-yr Government Bond Yields

US 10 yrCdn 10 yr

%

23

International Interest Parity Conditions

- How will exchange rates, domestic and foreign yields be linked?

- Text: discusses this in Ch. 18 (see pp. 481-483)

Uncovered Interest Parity:

- Canadian lender wants to lend for one year.

Option 1: Buy a one-year Canadian bond yield:ic (ic = .05 if rate is 5%)

Invest $1 in this option and get:

(1+ic) in one year.

Option 2: Buy a one-year American bond U.S. Yield:

iu

- Invest $1 Canadian in this ( 1/X0 U.S. dollars)

- X0 = exchange rate ($Cdn per U.S. dollar) at the time the bond is purchased.

- After one year lender receives:

(1+iu)x (1/X0) in U.S. dollars

- Convert to Cdn. dollars at the exchange rate at maturity (X1) gives:

(1+iu)x (X1/X0)

- note that X1: will be the future expected exchange rate.

24

- For equilibrium lenders must receive the same payoff under the two options (other things equal):

(1+ic) = (1+iu) x (X1/X0)

X1/X0 = 1+(X1-X0)/X0

i.e., 1 plus the proportional change in the exchange rate

(1+ic) = (1+iu)x (1+ Proportional Change in X)

- Approximation?

ic = iu + (Proportional Change in X)

- So unlike the, small open economy model ic does not always equal iu.

- equality if exchange rate is not expected to change

- Canadian yield lower if exchange rate is expected to fall (appreciation).

- Fall in X means U.S. dollars fall in value during the period

- decreases the return to the Cdn. investors in U.S. bonds

- raises the return to U.S. investors in Canadian bonds.

- Cdn. yields can be lower than U.S. yields and be as attractive.

25

- Canadian yield higher if exchange rate is expected to rise (depreciation).

- U.S. dollars rise in value during the holding period

- a source of extra return to the Cdn. investors in U.S. bonds

- reduces returns to Americans buying Canadian bonds.

- Cdn. yields must be higher than U.S. yields to be as attractive.

- Flows of cross border lending ensure that this condition holds:

- If the Canadian bond is not as attractive as a similar U.S. bond:

- Cdn. and U.S. lenders will not buy it

- its price falls, ic rises until the Cdn. bond is as attractive as the U.S. bond.

- If the Canadian bond is more attractive than the U.S. bond:

- lenders flock to the Canadian bond

- drives up its price and drives down ic

i.e., until the Cdn. bond is just as attractive as the U.S. bond.

26

- Exchange rate changes can play a part in bringing about the equilibrium:

- Say U.S. bond is the more attractive option:

- Cdn. lenders buy U.S. dollars

- X0 rises (price of U.S. dollar)

- Expected future change in E will now be smaller than before

- This reduces the attractiveness of the U.S. bond.

- In the above it is assumed that the yield on the U.S. bond is constant: Cdns. small lenders in the U.S. bond market.

Covered Interest Parity

- A lender can eliminate the risk of an exchange rate change by using the forward market for foreign exchange.

e.g., Buy a contract to purchase Cdn. dollars with U.S. dollars in one year.

i.e., fix X1 at the time the US bond is bought.

- Equilibrium will now require:

(1+ic) = (1+iu)x (F/X0)

F = forward rate (Cdn dollars per US dollar)

F/X0 = (1+ Proportional Difference between the forward rate and X0)

27

Or, approximately:

ic = iu + (Proportional Difference between the forward rate and X0)

- If this does not hold:

- if not,

e.g., U.S. bond is more generous then lenders avoid Cdn. bonds, Cdn. bond prices fall and ic rises (as above)

- exchange rates can also adjust (and may adjust first!)

- R0 will tend to rise: greater supply of Cdn. dollars as Cdns. try to buy U.S. bonds

- F will tend to fall: greater demand for Cdn. dollars in one year as Cdns. convert back from U.S.

- Other possible factors behind international yield differentials?

- Barriers to cross-country financial flows?

- lack of knowledge and/or costs of knowledge ;

- questions of contract enforceability ;

- government policies: capital controls

- are inflows or outflows permitted?

28

Risk Premia and the Supply-Demand Framework

- Focus on actual observed yields.

- Risk is unattractive to lenders.

- clearly the case for “default risk”: payments expected < payments promised.

- arguably the case for risk as measured by “variance” of returns (assumes risk averse lenders and undiversifiable risk)

- risk averse lenders value a $ loss more than an equivalent $ gain.

- Say that two assets are identical in all respects except risk.

- If the yield on the safe asset (Rs) is the same as that of the risky asset (Rr):

Rs = Rr (at R0 in diagram)

- lenders will choose to hold the safe asset instead of the risky asset.

- as lenders move between assets:

Rs will fall (demand for safe asset shifts right)

Rr will rise (demand for riskier asset shifts left)

- this continues until Rr is sufficiently higher than Rs to compensate lenders for risk, i.e. an equilibrium risk premium is in place.

- Equilibrium:Rr = Rs + risk premium

(assume the equilibrium premium is a constant for now)

29

- Lender decisions ensure that this condition will hold.

Rr > Rs + risk premium - lenders move to the risky asset, Rr falls, Rs rises until Rr-Rs equals the required risk premium.

Rr < Rs + risk premium - lenders move to the safe asset, Rs falls, Rr rises until Rr-Rs equals the required risk premium.

- Interest rates differences will build in lender perceptions of asset risk.

- higher the risk, the higher the risk premium, the higher the yield.

- If relative riskiness and risk attitudes are not changing this premium will be stable and interest rates on assets of different riskiness will move together.

i.e. Rr = Rs + risk premium

- so with a stable premium a 1% rise in Rs goes with a 1% rise in Rr.

- If the risky asset becomes riskier the premium rises as lenders switch from the risky to the safe asset (Rs falls, Rr rises): see page 9.

30

- Private vs. government debt as an example:

- Lower risk a reason why government yields are usually below corporate yields.

- See text Fig. 7.2: yields on Government vs. Corporate bonds (long-term).

- Here is Federal Treasury Bill vs. Corporate Paper (yields in %):

Jan-02

Aug-02

Mar-03Oct-

03

May-04

Dec-04Jul-0

5

Feb-06

Sep-06Apr-0

7

Nov-07Jun-08

Jan-09

Aug-09

Mar-10Oct-

10

May-11

Dec-11Jul-1

2

Feb-13

Sep-13Apr-1

4

Nov-14Jun-15

Jan-16

Aug-16

Mar-17Oct-

17

May-18

-1

0

1

2

3

4

5

6

3 Month Corporate Paper & T-Bill Yields 2002-2018

Corporate Paper T-Bill Paper - Tbill

31

- Bond rating agencies.

- Canada: Standard and Poor's, Dominion Bond Rating Service, Moodys, Fitch- rate government and corporate debt according to risk.

- low-risk ratings are associated with lower yields (see text Table 6-1).

- diagram below shows US corporate bond yields by ratings (AAA – low risk; BBB – medium risk; BB higher risk):

- Generally: - rates move together.

- how to explain periods where this is not so? Changes in riskiness.

32

- Risk structure of yields changes as perceived risk changes.

- Recessions of early-1980s and early-1990s - risk premium on corporate debt rose.

- Enron scandal spread on corporate bonds with different risk ratings. - old ratings regarded as less reliable: risk premia rose.

- Recent financial crisis:- August 2007 and sub-prime crisis (problems at BNP Paribas & Bear-

Stearns becomes public).- unclear who holds the “bad” mortgages.

- difference in yields on 3-month T-Bills and 3-month Corporate Paper jumps:

T-Bill Paper Spread (difference) July 18, 2007 4.54% 4.64% 0.10% Aug. 22, 2007 3.96% 5.05% 1.09%

- Lehman Brothers collapse (Sept. 2008): further rise in rick premia.

(see graph on p. 5)

33

- European government debt: Greek vs German government bonds

- Falling risk premium initially (Euro, greater economic integration, optimism that Greece will grow)

- Eurozone crisis, Greek debt problems and exploding risk premium.

34

- Supply-Demand and changing risk structure:

- initial premium (Rr-Rs) is just sufficient to compensate lenders for risk.

- say perceived riskiness rises: lenders shift from the risky to the safe asset until a new, larger risk premium sufficient to compensate them for the higher level of risk is in place.

- notice that the yields in this case move in different directions.

- Risk structure of interest rates and information:

- observed yield differentials reflect lender assessment of relative riskiness.

- builds in market expectations of things like default probabilities and undiversifiable risk.

35

Liquidity premia and Interest Rate Structure:

- Can be modeled the same way as risk premia.

- Liquid assets: can be easily converted into money at a "fair" price.e.g. via an active resale market.

- Liquidity is another characteristic that lenders value: - two assets identical except one is more liquid; - less liquid asset will pay a premium.

- Liquidity and risk: could treat the liquidity premium as part of the risk premium.

e.g. illiquid asset has a riskier resale price.

- Financial crises and liquidity: some markets “freeze up” – no buyers (lenders).

- liquidity premia rise.

36

37