Slide Presentations for Week 2

• Housing Data

• Basic Valuation (Present Value)

• Debt Data

• Return to Equity Holder and Role of Leverage

• Federal and Sector Debt

• Macro Accounting Basics

• Federal Funds and Discount Rate

• Supply and Demand for Bank Reserves

• Short-term Interest Rates and Mortgage Rate

• Supply and Demand for Bonds

• Long Term Interest Rates and Spread

• Supply and Demand for Interest Rate Spreads

• Two Assets: the role of correlation

Case-Shiller Housing Index

020406080

100120140160180200

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

Annual Change (%)

-25.00%

-20.00%

-15.00%

-10.00%

-5.00%

0.00%

5.00%

10.00%

15.00%

20.00%19

88

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

Quarterly Change (%)

-8.00%

-6.00%

-4.00%

-2.00%

0.00%

2.00%

4.00%

6.00%

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010

Homebuyers were Crazy, Nuts, …?

Basics of Asset Valuation The value of an asset is the risk adjusted present value of all future net benefits.

L+

++

++

+= 3

32

21

1

)1()1()1( kNB

kNB

kNBValue

where, NB is Net Benefit k is the discount rate superscripts denote the time dimension (e.g., 1 year, 2 year, etc.)

Housing Example Individual is considering purchasing a $100,000 home, with plans to sell the home in 3 years. The mortgage rate is 5%. Scenario 1: Individual expects the house to appreciate 5% per year.

Value of Home = 000,100$)05.1(50.762,115$3 =

+

Scenario 2: Individual expects the house to appreciate 10% per year.

Value of Home = 80.976,114$)05.1(

100,133$3 =

+

Scenario 3: Individual expects the house to appreciate 15% per year.

Value of Home = 90.378,131$)05.1(50.087,152$3 =

+

Household Debt to Disposable Income

0.0%

20.0%

40.0%

60.0%

80.0%

100.0%

120.0%

140.0%

1946

1950

1954

1958

1962

1966

1970

1974

1978

1982

1986

1990

1994

1998

2002

2006

Total Debt/IncomeMortgage Debt/IncomeConsumer Credit/Income

Debt Service (DSR) and Financial Obligations (FOR) Ratios

6.00%

8.00%

10.00%

12.00%

14.00%

16.00%

18.00%

20.00%

1980

Q119

81Q3

1983

Q119

84Q3

1986

Q119

87Q3

1989

Q119

90Q3

1992

Q119

93Q3

1995

Q119

96Q3

1998

Q119

99Q3

2001

Q120

02Q3

2004

Q120

05Q3

2007

Q120

08Q3

DSRFOR

The household debt service ratio (DSR) is an estimate of the ratio of debt payments to disposable personal income. Debt payments consist of the estimated required payments on outstanding mortgage and consumer debt. The financial obligations ratio (FOR) adds automobile lease payments, rental payments on tenant-occupied property, homeowners' insurance, and property tax payments to the debt service ratio.

Homeowners Financial Oblgiation Ratios by Type

4.00%

6.00%

8.00%

10.00%

12.00%

14.00%

16.00%

18.00%19

80Q

1

1981

Q3

1983

Q1

1984

Q3

1986

Q1

1987

Q3

1989

Q1

1990

Q3

1992

Q1

1993

Q3

1995

Q1

1996

Q3

1998

Q1

1999

Q3

2001

Q1

2002

Q3

2004

Q1

2005

Q3

2007

Q1

2008

Q3

TotalMortgageConsumer

Homeowner and renter FORs are calculated by applying homeowner and renter shares of payments and income derived from the Survey of Consumer Finances and Current Population Survey to the numerator and denominator of the FOR. The homeowner mortgage FOR includes payments on mortgage debt, homeowners' insurance, and property taxes, while the homeowner consumer FOR includes payments on consumer debt and automobile leases.

Too Much Debt? Why the increase in leverage?

Leverage: Upside and Downside

Example: Home Buying

Purchase price = $100,000 Interest Rate = 10%

Financing Options

Option 1: Finance with your own cash (no debt) Option 2: Finance half with cash and half with mortgage Option 3: Finance 20% cash and 80% mortgage

Assuming you sell the house after one year for $120,000, what is your profit and rate of return for each financing option?

Option 1: Finance with your own cash (no debt)

Investment (equity) = $100,000

Mortgage (debt) = $0

Debt-Equity = 0

Profit = Sale Price – Purchase Price

= $120,000 - $100,000 = $20,000

Rate of return = %2010020.100000,100$

000,100$000,120$=×=×

−

Option 2: Half Mortgage, Half Cash (D/E = 1)

Investment (equity) = $50,000 Mortgage (debt) = $50,000 (interest payment = $5,000) Debt-Equity = 1

Profit = Sale Price – Purchase Price – Interest Payment

= $120,000 - $100,000 - $5,000 = $15,000

Rate of return = %3010030.100000,50$

000,5$000,100$000,120$=×=×

−−

Option 3: Finance 20% cash and 80% mortgage (D/E = 4) Investment (equity) = $20,000 Mortgage (debt) = $80,000 (interest payment = $8,000) Debt-Equity = 4

Profit = $120,000 - $100,000 - $8,000 = $12,000

Rate of Return = %6010060.100000,20$

000,8$000,100$000,120$=×=×

−−

Upside and Downside of Leverage

-200%

-150%

-100%

-50%

0%

50%

100%

150%

200%

250%$8

0,00

0$8

4,00

0$8

8,00

0$9

2,00

0$9

6,00

0$1

00,0

00$1

04,0

00$1

08,0

00$1

12,0

00$1

16,0

00$1

20,0

00$1

24,0

00$1

28,0

00$1

32,0

00$1

36,0

00$1

40,0

00$1

44,0

00$1

48,0

00

Sale Price

Rat

e of

Ret

urn

Option 1Option 2Option 3

Rate of Return on Equity (Modigliani-Miller)

Option 1: D/E = 0 → rate of return = 20%

Option 2: D/E =1 → rate of return = 30%

Option 3: D/E = 4 → rate of return = 60%

How does the rate of return on the homebuyer’s equity relate to the appreciation of the asset (Home) and financing costs?

EDiRRrr

VEi

VDR AAEEA )( −+=→+=

RA is the return on the asset (appreciation/depreciation of the home) rE is the return to the equity holder (homeowner) i is the interest rate (mortgage rate) D is the amount of debt E is the amount of Equity V is the book value of the asset (thus, V = D + E)

Rate of Return on Equity

Option 1: D/E = 0

%200%)10%20(%20)( =×−+=−+=EDiRRr AAE

Option 2: D/E =1

%301%)10%20(%20)( =×−+=−+=EDiRRr AAE

Option 3: D/E = 4

%604%)10%20(%20)( =×−+=−+=EDiRRr AAE

Rate of Return on Equity

EDiRRr AAE )( −+=

“Financial Risk” “Business Risk”

U.S. Federal Debt as Percent of GDP

20.0

40.0

60.0

80.0

100.0

120.0

1940

1943

1946

1949

1952

1955

1958

1961

1964

1967

1970

1973

1976

1979

1982

1985

1988

1991

1994

1997

2000

2003

2006

2009

Gross Federal DebtHeld by Public

Annual Debt Growth Rates by Sector

-10

-5

0

5

10

15

20

25

30

1980

1982

1984

1986

1988

1990

1992

1994

1996

1998

2000

2002

2004

2006

2008

HouseholdsCorporate BusinessFederal Gov't

U.S. Shares in Income

10.00%15.00%20.00%25.00%30.00%35.00%40.00%45.00%50.00%55.00%60.00%

1947

1950

1953

1956

1959

1962

1965

1968

1971

1974

1977

1980

1983

1986

1989

1992

1995

1998

2001

2004

2007

Wage ShareProfit Share

A little Macro Accounting

Expenditures Use of Income C + I + G + X = C + S + T + M Cancelling consumption… Injections Leakages I + G + X = S + T + M and, grouping… Private Public Foreign Sector Sector Sector Balance Balance Balance (I – S) + (G – T) + (X – M) = 0 Definitions: C – Consumption S - Savings I – Investment T - Taxes G – Government M - Imports X - Exports

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00Ja

n-90

Jan-

91

Jan-

92

Jan-

93

Jan-

94

Jan-

95

Jan-

96

Jan-

97

Jan-

98

Jan-

99

Jan-

00

Jan-

01

Jan-

02

Jan-

03

Jan-

04

Jan-

05

Jan-

06

Jan-

07

Jan-

08

Jan-

09

Jan-

10

FEDFUNDSDiscount Rate

Bank Reserves (R)

dr

ff

DR

SR

FedFunds (ff), DiscountRate (dr)

Bank Reserves (R)

3%

2%

DR

SR

1.5%

1

2

FedFunds (ff), DiscountRate (dr)

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

Jan-

97

Jan-

98

Jan-

99

Jan-

00

Jan-

01

Jan-

02

Jan-

03

Jan-

04

Jan-

05

Jan-

06

Jan-

07

Jan-

08

Jan-

09

Jan-

10

3 M T- BillCPF3MCPN3M

3 M T-Bill is the interest rate on a 3 month Treasury Bill CPF3M is the interest rate on 3 month financial corporate paper CPN3m is the interest rate on 3 month NON-financial corporate paper

0.00

1.00

2.00

3.00

4.00

5.00

6.00

Jan-0

7Apr-

07Ju

l-07

Oct-07

Jan-0

8Apr-

08Ju

l-08

Oct-08

Jan-0

9Apr-

09Ju

l-09

Oct-09

Jan-1

0Apr-

10Ju

l-10

Oct-10

3 M T- BillCPF3MCPN3M

Interest Rate spreads widened…What would it mean?

30 Year Mortgage Rate - Conventional

3.50

4.50

5.50

6.50

7.50

8.50

9.50

Jan-

00

Jul-0

0

Jan-

01

Jul-0

1

Jan-

02

Jul-0

2

Jan-

03

Jul-0

3

Jan-

04

Jul-0

4

Jan-

05

Jul-0

5

Jan-

06

Jul-0

6

Jan-

07

Jul-0

7

Jan-

08

Jul-0

8

Jan-

09

Jul-0

9

Jan-

10

Jul-1

0

Bond Prices and Interest Rates

To take the simplest type of bond, assume a bond promises to make one payment of $1,000 in one year. If we ask how much an individual will pay for the bond today, then they will have to assign an appropriate interest rate to be used in the present value calculation. Suppose the individual tells us that they demand a 5% interest rate in order to purchase this bond. What will be the maximum price they would be willing to pay?

38.952$05.1

000,1$)1(

=+

=+

=r

FVPV

Notice what happens if our individual decides that they only demand a 3% interest rate in order to buy the bond.

87.970$03.1

000,1$)1(

=+

=+

=r

FVPV

What if they demand a 7% interest rate?

58.934$07.1

000,1$)1(

=+

=+

=r

FVPV

As the interest rate increases from 3% to 5% to 7%, the price the individual would be will to pay for the

bond would decrease from $970.87 to $952.38 to $934.58.

Price of Bond Interest Rate

3%

5%

7%

$970.87

$934.58

$952.38

Price of Bond Interest Rate

5% $952

S

D

3%

7%

$970

$934

An increase in the demand for bonds leads to an increase in Price and decrease in the interest rate…

Price of Bond Interest Rate

5% $952

S

D1

3%

7%

$970

$934 D2

A decrease in the demand for bonds leads to a decrease in Price and increase in the interest rate…

Price of Bond Interest Rate

5% $952

S

D1

3%

7%

$970

$934

D2

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

Jan-

90

Jan-

91

Jan-

92

Jan-

93

Jan-

94

Jan-

95

Jan-

96

Jan-

97

Jan-

98

Jan-

99

Jan-

00

Jan-

01

Jan-

02

Jan-

03

Jan-

04

Jan-

05

Jan-

06

Jan-

07

Jan-

08

Jan-

09

Jan-

10

GS1GS5GS10

GS1 is the interest rate on a 1 year U.S. Government Bond GS5 is the interest rate on a 5 year U.S. Government Bond GS10 is the interest rate on a 10 year U.S. Government Bond

0.00

1.00

2.00

3.00

4.00

5.00

6.00

Feb-06

May-06

Aug-06

Nov-06

Feb-07

May-07

Aug-07

Nov-07

Feb-08

May-08

Aug-08

Nov-08

Feb-09

May-09

Aug-09

Nov-09

Feb-10

May-10

Aug-10

Nov-10

GS1GS5GS10GS30

0.00

2.00

4.00

6.00

8.00

10.00

12.00

Jan-

90

Jan-

91

Jan-

92

Jan-

93

Jan-

94

Jan-

95

Jan-

96

Jan-

97

Jan-

98

Jan-

99

Jan-

00

Jan-

01

Jan-

02

Jan-

03

Jan-

04

Jan-

05

Jan-

06

Jan-

07

Jan-

08

Jan-

09

Jan-

10

AAABAA

AAA is the interest rate on AAA rated corporate bonds BAA is the interest rate on BAA rate corporate bonds

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

9.00

10.00

Jan-

07

Mar

-07

May

-07

Jul-0

7

Sep

-07

Nov

-07

Jan-

08

Mar

-08

May

-08

Jul-0

8

Sep

-08

Nov

-08

Jan-

09

Mar

-09

May

-09

Jul-0

9

Sep

-09

Nov

-09

Jan-

10

Mar

-10

May

-10

Jul-1

0

Sep

-10

Nov

-10

AAABAA

Spread between BAA-AAA

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00Ja

n-90

Jan-

91

Jan-

92

Jan-

93

Jan-

94

Jan-

95

Jan-

96

Jan-

97

Jan-

98

Jan-

99

Jan-

00

Jan-

01

Jan-

02

Jan-

03

Jan-

04

Jan-

05

Jan-

06

Jan-

07

Jan-

08

Jan-

09

Jan-

10

Spread for BAA-GS10

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

Jan-

90

Jan-

91

Jan-

92

Jan-

93

Jan-

94

Jan-

95

Jan-

96

Jan-

97

Jan-

98

Jan-

99

Jan-

00

Jan-

01

Jan-

02

Jan-

03

Jan-

04

Jan-

05

Jan-

06

Jan-

07

Jan-

08

Jan-

09

Jan-

10

Interest Rate Spreads

S S

D D

4%

6%

10-Year U.S. Government Bond 10-Year Corporate Bond

P P i i

S S

D D

5%

7%

AAA Corporate Bond Baa Corporate Bond

P P i i

Expected Returns and Risk: The Role of Correlation

Suppose an investor has a total of $100,000 to invest in a stock and/or bond. The investor must decide how much of the $100,000 to invest in the stock and how much to invest in the bond.

Stock Bond

Expected Return E(r) 7.50% 5.00%

Standard Deviation of Returns (σ) 12.50% 5.00%

Correlation (ρ) -1 Suppose the investor held only the bond. The expected return would be 5% with a standard deviation of 5%. Dissatisfied with this return and willing to take on more risk if necessary, the investor sells some bonds and invests in the stock. Suppose the investor’s new portfolio contained 30% stocks and 70% bonds. What is the expected rate of return on the investor’s portfolio? The expected rate of return on a portfolio is merely the weighted average of the individual rates of returns – where the weights are the percentage of the asset in the portfolio.

)()()( BBssp rEWrEWrE += The W’s represent the weights (or, percentage of the asset in the portfolio) and subscripts S and B refer to stock and bond respectively. In our example, the expected rate of return on the portfolio is calculated as follows.

%75.5)5)(7(.)5.7)(3(.)()()( =+=+= BBssp rEWrEWrE Hence, the investor has been able to increase the expected rate of return on the portfolio by holding some stock.

What was the cost of obtaining the higher expected rate of return? The investor may have believed that he would have to take on more risk (i.e., higher standard deviation) to obtain a higher expected return. However, did risk increase? In order to calculate the standard deviation of the portfolio we begin by calculating the variance of a portfolio.

ρσσσσσ BsBsBBssP WWWW 2)()( 222 ++= The Greek letter rho (ρ) is the correlation coefficient – which when multiplied by the two standard deviations equals the covariance between the two assets. The important point to notice about the above equation for the variance is that unlike the expected rate of return it is not – at least not always – the simple weighted average of the individual variances. In our example, the variance of the portfolio composed of 30% stock and 70% bonds is the following.

0625.)1)(5)(5.12)(7)(.3(.2)]5)(7[(.)]5.12)(3[(.

2)()(

22

222

=−++=

++= ρσσσσσ BsBsBBssP WWWW

The standard deviation of the portfolio (i.e., our measure of risk) is the square root of the variance.

%25.0625.2 === PP σσ By adding an asset (i.e., the stock) with a higher rate of return and risk to his bond-only portfolio our investor has been able to increase the expected rate of return – not very surprising – and reduce the overall risk of the portfolio – this is very surprising. We can observe the impact by looking at how things change when we alter the percentage of each asset held.

Stock Bond Return (%) Risk (%) 100% 0% 7.5 12.595% 5% 7.375 11.62590% 10% 7.25 10.7585% 15% 7.125 9.87580% 20% 7 975% 25% 6.875 8.12570% 30% 6.75 7.2565% 35% 6.625 6.37560% 40% 6.5 5.555% 45% 6.375 4.62550% 50% 6.25 3.7545% 55% 6.125 2.87540% 60% 6 235% 65% 5.875 1.12530% 70% 5.75 0.2525% 75% 5.625 0.62520% 80% 5.5 1.515% 85% 5.375 2.37510% 90% 5.25 3.255% 95% 5.125 4.1250% 100% 5 5

Graphically…..

Figure 5.1- The Efficient Frontier

4.00

4.50

5.00

5.50

6.00

6.50

7.00

7.50

8.00

0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00

Risk

Ret

urn

The role of the correlation between 2 assets

Correlation = +1

5

6

7

8

9

10

11

0 5 10 15 20 25 30

Risk

Retu

rn

Correlation = +0.5

5

6

7

8

9

10

11

0 5 10 15 20 25 30

Risk

Retu

rn

Correlation = -0.5

5

6

7

8

9

10

11

0 5 10 15 20 25 30

Risk

Retu

rn

Correlation = -1

5

6

7

8

9

10

11

0 5 10 15 20 25 30

Risk

Retu

rn