Chapter 6: Interest Rates

Topics covered

• Cost of Money (Introduction)• Factors affecting cost of money

– Fundamental factors– Macroeconomic factors

• Interest rate levels• Determinants of market interest rates• Term structure of interest rates• What determines the shape of the yield curve?

– Analysis of the impact of different factors (inflation risk, maturity risk, liquidity risk, default risk) on the shape of yield curves for treasury and corporate securities

• Risks associated with investment in overseas securities

Answers to selected problems

• 6-2 (2.25%)• 6-3 (2 yr: 6%, 3 yr: 6.33%)• 6-4 (1.5%)• 6-5 (0.2%)• 6-9 (6.8%)• 6-11 (1.55%)• 6-12 (0.35%)• 6-13 (1.775%)

Self-Test (Page 187 and 188)

• Attempt Self-Test 1 page 187 • Attempt Self-Test 2 page 188

– Answersa) 2.5%b) 5.8%c) 7.6%d) 6.95%e) 8.75%f) 5.5%

• Hint: Inflation Premium = 26 + x / 9 » Everything else is given in question just put those values in formula

for calculating interest rate for T-bond and calculate X.

1. INTRODUCTION

Cost of money is the rental price of borrowing money

Suppose you go to a bank to borrow $10,000 for paying off college fees, you won’t be able to get this money for free.

The $10,000 come with a price tag attached, i.e. some rate of interest, consider for example a 10% rate of interest.

This 10% interest rate is the cost of obtaining $10,000. This cost is also known as the ‘cost of money’.

LENDERS BORROWERS

EXCESS FUNDS

PRICING SYSTEM (i)

Supply of funds

Demand of funds

$

i

i

In a free economy, excess funds of lenders are allocated to borrowers through a pricing system based on the supply of and demand for funds. This pricing system is represented by interest rates, ‘i’ or the cost of money.

So, Now we know!

• Supply and demand of funds determines the interest rates (i).

• It is by providing these rates that the borrowers make use of the funds provided by the lenders.

• Generally interest rates are believed to be the cost of money.

• However, in case of equity capital,– Cost of money is called ‘Cost of equity’ and it

consists of dividends and capital gains expected by the share holders

– Cost of equity = Dividends + Capital Gains

Remember!

• Cost from fund users’ perspectiveCost of

Money • Return from fund

providers’ perspectiveCost of Money

BANK(PROVIDER)

CORPORATION ABC

(USER)

DEBTCAPITAL

MONEY

COST OF MONEY (i)

Return for the funds provider Cost for the user of funds

STOCK-HOLDERS(PROVIDER)

CORPORATION ABC

(USER)

MONEY

COST OF MONEY (D+C.G.)

Return for the funds provider Cost for the user of funds

EQUITYCAPITAL

QUICK FLASHBACK!

• ‘i’ is the cost of obtaining money.

• Supply and demand of funds determines the interest rates.

2. Factors affecting cost of money, ‘i’

The four most fundamental factors affecting the cost of money are: 1. Production opportunities

– Rate of return that producers expect to earn on invested capital.

2. Time preferences for consumption– The preferences of consumers for current consumption as opposed to saving for

future consumption. Preference for current consumption Supply of funds Interest rate

3. Riskiness of loan– The chance that an investment will provide a low or negative return.

4. Inflation– The amount by which prices increase over time. Expected Inflation Demand of funds Interest rate

For highly risky loans investors expect high

rate of return, i.e. high ‘i’

i. Fundamental factors affecting cost of money, ‘i’

ii. Macroeconomic factors affecting cost of money, ‘i’

1. Monetary policy tools– Federal Reserve Policies– Open Market Operations

2. Business boom3. Business recession4. Government budget deficit and surplus

1. Federal Reserve Policies– An increase in required reserve ratio by central

bank means reduction in volume of deposits which raises interest rates.

RRR Supply of funds Interest rate

– A decrease in required reserve ratio means availability of excess deposits which decreases interest rates.

RRR Supply of funds Interest rate

2. Open Market Operations– Central bank buys back securities from open

market thus injecting money into the system (increasing supply of money) which decreases interest rates.

– Central bank sells securities into open market thus absorbs money from the system (decreasing supply of money) which increases interest rates.

3. Business boomsIncreased demand of funds Inflationary pressures i

4. Business recessionDecreased demand of funds Inflationary pressures i

5. Government budget deficitGovernment needs funds which means demand for funds i

6. Government budget surplusGovernment does not need funds which means demand for funds i

3. INTEREST RATE LEVELS

• Capital is allocated to borrowers according to interest rates, i. – Most capital across the world is allocated through the price system (that is,

interest rate).

• As can be seen in the figure below the excess funds of lenders are allocated to the borrowers through a price system that is the interest rate.

INTEREST RATE LEVELS• The firms with the most profitable investment opportunities are

willing and able to pay the most for capital, so they tend to attract it away from inefficient firms and firms whose products are not in demand.

• There are many different types of capital markets (for example, market for high risk securities, market for low risk securities etc.) and they are all interconnected.

• Interdependence of capital markets– Capital markets are interdependent, i.e. changes in supply and demand

of funds in one market are going to produce an impact on the supply and demand of funds in the other market/s.

4. Determinants of Market Interest Rates

• The interest rate quoted on any debt security is composed of a real risk-free rate, r* , plus several premiums that reflect inflation, the security’s risk, its liquidity (or marketability), and the years to its maturity. This relationship can be expressed as follows:

Quoted interest rate = r = r* + IP + DRP + LP + MRP

How is interest rate determined on debt securities?

• Required Rate of Return– Nominal rate of return an investor requires to

make an investment worthwhile.– Made up of 3 components:• Real risk free rate• Inflation premium• Risk premium

Formulas

• Interest rate on short-term govt. security• Interest rate on long-term govt. security• Interest rate on corporate securities

• (lecture)

1. Real risk free rate of return, r*

• Definition– r* is the minimum rate of return an investor

requires. This rate does not take into account expected inflation.

• Changes in r*• r* is equal to T-bill rate minus the inflation

premium.

2. Inflation Premium

• Inflation– Definition: Loss in purchasing power of money

because of increase in prices.– As inflation increases every dollar we own buys a

smaller percentage of goods and services.• Why is inflation premium given?• Impact of inflation on treasury and corporate

securities• Calculation

Risk Free Rate

• rRF = r* + IP. It is the quoted rate on a risk-free security such as a Treasury bill and it includes a premium for expected inflation.

Difference between Real Risk free interest rate and Risk free interest rate

• Risk free interest rate = Real Risk free interest rate + Inflation premium• Real Risk free interest rate = Risk free interest rate – Inflation premium

• What does the term ‘real’ means?• What does the term ‘risk-free’ means?

3. Risk Premiums

1. DRP = default risk premium. This premium reflects the possibility that the issuer will not pay the promised interest or principal at the stated time.

1. Treasury securities have no chance of default hence DRP isn’t paid on them.

2. For corporate bonds higher the bonds rating, lower its default risk and lower will be the interest rates.

3. Risk Premiums

2. LP: Liquidity Premium.– Liquid asset: An asset that can be converted to

cash quickly at a fair market value.– Liquidity premium is added to ROI on securities

that aren’t liquid.

– Liquidity premium for treasury and corporate securities

3. Risk Premiums3. MRP = Maturity Risk Premium. Longer-term bonds, even

Treasury bonds, are exposed to a significant risk of price declines due to increases in interest rates; and a maturity risk premium is charged by lenders to reflect the interest rate risk.

MRP is paid to cover interest rate risk.– Interest rate risk: The risk of capital losses to which investors are

exposed because of changing interest rates.

While long term bonds are exposed to interest rate risk, short term bonds are exposed to reinvestment rate risk.– Reinvestment rate risk: The risk that a decline in interest rates will

lead to lower income when bonds mature and funds are reinvested.

Simple Problems

• If expected inflation during the next year is 2% and currently the nominal interest rate on T-bills is 5%, what is the real risk free rate of interest?

• If inflation is expected to average 4% during the next year and the real risk free rate of interest is 3%, what should be the nominal rate of interest?

• Answers: 3% and 7%

Simple Problem

• Assume that the real risk free rate, r* = 2% and the average expected inflation rate is 3% for each future year. The DRP and LP for Bond X are each 1% and the applicable MRP is 2%.– What is Bond X’s interest rate?– Is Bond X a treasury bond or a corporate bond?– Does Bond X more likely to have a 3 month or 20 year

maturity?

– Answers: 9%, corporate, 20 year

5. Term Structure of Interest Rates• TSIR describes the relationship bond yields and maturities.• Yield Curve

– Yield curve is actually a graph showing relationship between bond yields and maturities.

• TSIR enables investors to quickly compare the yields offered on short-term, medium-term and long-term bonds

• Three different types of Yield Curves:– “Normal” Yield Curve

• Upward sloping yield curve• Short term interest rates are low, long term interest rates are high.

– Inverted (“Abnormal”) Yield Curve • Downward sloping yield curve• Short term interest rates are high, long term interest rates are low.

– Humped yield curve • A yield curve where interest rates on medium-term maturities are higher than rates on both short-and

long-term maturities.

• Why does it matter?

6. What determines the shape of the yield curve?

Factors affecting shape of treasury securities• Yield on a Treasury bond that matures in t years can be expressed as follows:

– T-bond yield = r* + IPt + MRPt

• It thus emerges that expected inflation levels and bond’s maturity are the main factors affecting shape of yield curve of treasury securities. (Value of real risk free rate of interest, r* varies somewhat over time because of changes in the economy and demographics, these changes are random rather than predictable, r* thus is assumed to remain constant.)

• Inflation• Expected inflation has an important effect on the yield curve for treasury securities. If

the market expects inflation to increase in the future, the inflation premium will be higher on a 3-year bond than on a 1-year bond. On the other hand, if the market expects inflation to decline in the future, long-term bonds will have a smaller inflation premium than will short-term bonds.

• Maturity• Since investors consider long-term bonds to be riskier than short-term bonds because

of interest rate risk, the maturity risk premium always increases with maturity.

When inflation is expected to increase

• Long term bonds have higher yields for 2 reasons:– Inflation is expected to be higher in

future• If market expects inflation to increase in

future, the inflation premium will be higher the longer the term to maturity.

– Positive MRP• MRP always increases with increasing

maturity of bond.

– Refer to table page 177

• When inflation is expected to decrease

• If market expects inflation to decline in future, long-term bonds will have smaller inflation premium (thus lower rates) than short-term bonds.

• Such yield curves predict economic downturn because weaker economic conditions generally lead to declining inflation which leads to lower long-term interest rates.

Factors affecting shape of Corporate bonds

• Corporate bonds include a default risk premium (DRP) and a liquidity premium (LP). Therefore, the yield on a corporate bond that matures in t years can be expressed as follows:

• Corporate bond yield = r* + IPt + DRPt + LPt + MRPt

• The corporate bonds carry additional default and liquidity risks, this is the reason they pay premium for covering these risks which is why the ‘i’ (interest rate) paid on corporate bond, also called the yield, is always higher than that paid on treasury bonds.

Because of their additional default and liquidity risk, corporate bonds yield more than treasury bonds with the same maturity and BBB-rated bonds yield more than AA-rated bonds.

• Corporate bond yield can be calculated using the formula:

• r = r* + IPt + DRPt + LPt + MRPt

• LP and DRP of a corporate bond are affected by its maturity• For example:– Coca Cola's chances of defaulting on 10 years bond are less

as compared to defaulting on a 100 year bond, so higher DRP is paid on the bond with ______ years to maturity?

• Long term bonds are also less liquid than short term bonds so as maturity of bonds increases LP also increases.

7. Risks associated with investment in overseas securities

• Two main types of risks that an investor, looking to invest in foreign securities, faces are: country risk and exchange rate risk.

• Country risk– Risk that arises from investing or doing business in

a particular country– This risk depends on a country’s economic, social

and political environment. – Countries with safer political, social and economic

environment have less country risk and therefore are safe choices for overseas investment.

• Exchange rate risk– Risk of losing money in local currency because of fluctuation in

the value of foreign currency (in which investment was being made).

– Recall example narrated in class (Pakistani earning US dollars and praying for weak Pakistani rupee relative to US dollar).

– Suppose a US investor purchases Japanese bond. The US investor gets interest rate in Japanese currency (Yen) which must then be converted into US dollars whenever he wants to make a purchase (as the investor resides in the US). Whenever Yen strengthens in comparison to dollar it means Yen can be converted into a larger number of US dollars and the investor will be better off. On the other hand if Yen weakens relative to dollar, it would mean Yen’s conversion into dollar will give off fewer dollars and the investor will have to suffer.

Interest rate determination

• Formula for calculation of interest rate on short term treasury securities:– Quoted interest rate = Real risk free rate + inflation premium

– r = r* + IPt • Formula for calculation of interest rate on long

term treasury securities:– Quoted interest rate = Real risk free rate + inflation premium +

maturity risk premium

– r = r* + IPt + MRPt

Interest rate determination

• Formula for calculation of interest rate on corporate securities:

– r = r* + IPt + DRPt + LPt + MRPt – Quoted interest rate = Real risk free rate + inflation premium + default

risk premium + liquidity premium + maturity risk premium