Capital markets

Capital Markets

Savings, Investment, and Interest Rates

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Some Useful Terminology

• Savings: Current income which is deferred for future consumption (i.e., not spent)

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Some Useful Terminology

• Savings: Current income which is deferred for future consumption (i.e., not spent)

National Income: $8,512.3 B

+ Dividend Payments, Interest, Gov’t Transfers, etc.: $582.5B

- Taxes: $1,077.2 B

= Personal Disposable Income: $8,017.6 B

- Personal Consumption Expenditures: $7,727.2 B

= Personal Savings: $290.4B (3.5% of Personal Income)

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Some Useful Terminology

• Savings: Current income which is deferred for future consumption (i.e., not spent)

National Income: $8,512.3 B

+ Dividend Payments, Interest, Gov’t Transfers, etc.: $582.5B

- Taxes: $1,077.2 B

= Personal Disposable Income: $8,017.6 B

- Personal Consumption Expenditures: $7,727.2 B

= Personal Savings: $290.4B (3.5% of Personal Income)

• Note that there are many ways to save (savings account, bonds, stocks, etc.)

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Some Useful Terminology

• Investment: The purchase of new capital goods.

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Some Useful Terminology

• Investment: The purchase of new capital goods.

– Gross Investment: Total purchases of new capital goods

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Some Useful Terminology

• Investment: The purchase of new capital goods.

– Gross Investment: Total purchases of new capital goods• Gross Private Investment: $1,611.2 B

• Gross Public Investment: $355 B

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Some Useful Terminology

• Investment: The purchase of new capital goods. – Gross Investment: Total purchases of new capital goods

• Gross Private Investment: $1,611.2 B• Gross Public Investment: $355 B

– Net Investment: Gross investment less depreciation of existing capital (capital consumption)

• Net Private Investment: $500 B• Net Public Investment: $250 B

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NIPA Accounts

• Recall, the accounting identity in the NIPA accounts: GDP = C + I + G + NX

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NIPA Accounts

• Recall, the accounting identity in the NIPA accounts: GDP = C + I + G + NX

• GDP = Gross Private Savings + Taxes + C

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NIPA Accounts

• Recall, the accounting identity in the NIPA accounts: GDP = C + I + G + NX

• GDP = Gross Private Savings + Taxes + C

Gross Private Savings = I + (G-T) + NX

I (Public + Private) : $1,966 B

+ (G-T): $106B

+ NX: - $559B

Gross Private Savings: $1,513B (16% of GDP)

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NIPA Accounts

• Recall, the accounting identity in the NIPA accounts: GDP = C + I + G + NX

• GDP = Gross Savings + Taxes + CI + (G-T) + NX = Gross Private Savings

I (Public + Private) : $1,966 B+ (G-T): $123B + NX: - $487B

Gross Private Savings: $1,513B

Personal Savings ($290B) = Gross Private Saving ($1,513B) - Depreciation

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Interest Rates

• What is an interest rate?

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Interest Rates

• What is an interest rate?– The interest rate is the relative price of current

spending in terms of foregone future income.

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Interest Rates

• What is an interest rate?– The interest rate is the relative price of current

spending in terms of foregone future income.– Example: if the interest rate is 5% (Annual),

you must give up $1.05 worth of next year’s income in order to increase this year’s spending by $1.

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Interest Rates:1987-2003

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Interest Rates:1987-2003

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The Yield Curve

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Yield Curves

• What determines the shape of the yield curve?– Segmented Markets Hypothesis– Expectations Hypothesis– Preferred Habitat Hypothesis

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Interest Rates

• Treasury Securities (1 - 5%)• Agency Securities (1 - 5%)• Municipal Bonds (3 – 5%)• Corporate Bonds (6 – 11%)• Preferred Stock (5 – 15%)• Asset Backed Securities (4 – 5%)

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Interest Rates

• Treasury Securities (1 - 5%)• Agency Securities (1 - 5%)• Municipal Bonds (3 – 5%)• Corporate Bonds (6 – 11%)• Preferred Stock (5 – 15%)• Asset Backed Securities (4 – 5%)

• “Risky” Rate = Risk Free Rate + Risk Premium

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Real vs. Nominal Interest Rates

• As with any other variable, the nominal interest rate is in terms of dollars. (the cost of a current dollar in terms of forgone future dollars). To calculate the real interest rate, we need to correct for the purchasing power of those dollars.

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Real vs. Nominal Interest Rates

• As with any other variable, the nominal interest rate is in terms of dollars. (the cost of a current dollar in terms of forgone future dollars). To calculate the real interest rate, we need to correct for the purchasing power of those dollars.

• Exact: (1+i ) = (1+ r )*(1 + inflation rate)

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Real vs. Nominal Interest Rates

• As with any other variable, the nominal interest rate is in terms of dollars. (the cost of a current dollar in terms of forgone future dollars). To calculate the real interest rate, we need to correct for the purchasing power of those dollars.

• Exact: (1+i ) = (1+ r )*(1 + inflation rate)

• Approximation: i = r + inflation rate

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Real/Nominal Interest Rates

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Real vs. Nominal Interest Rates

• As with any other variable, the nominal interest rate is in terms of dollars. (the cost of a current dollar in terms of forgone future dollars). To calculate the real interest rate, we need to correct for the purchasing power of those dollars.

• Exact: (1+i ) = (1+ r )*(1 + inflation rate)

• Approximation: i = r + inflation rate

• How can real interest rates be negative?

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Real vs. Nominal Interest Rates

• As with any other variable, the nominal interest rate is in terms of dollars. (the cost of a current dollar in terms of forgone future dollars). To calculate the real interest rate, we need to correct for the purchasing power of those dollars.

• Exact: (1+i ) = (1+ r )*(1 + inflation rate)

• Approximation: i = r + inflation rate

• How can real interest rates be negative?

– Ex ante vs. ex post

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Present Value

• With a positive interest rate, income received in the future is less valuable that income received immediately.

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Present Value

• With a positive interest rate, income received in the future is less valuable that income received immediately.

• At a 5% annual interest rate, $1.05 to be received in one year is equivalent to $1 to be received today (because $1 today could be worth $1.05)

$1(1.05) = $1.05

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Present Value

• With a positive interest rate, income received in the future is less valuable that income received immediately.

• At a 5% annual interest rate, $1.05 to be received in one year is equivalent to $1 to be received today (because $1 today could be worth $1.05)

$1(1.05) = $1.05

• Therefore, the present value of $1.05 to be paid in one year (if the annual interest rate is 5%) is $1.

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Present Value

• With a positive interest rate, income received in the future is less valuable that income received immediately.

• At a 5% annual interest rate, $1.05 to be received in one year is equivalent to $1 to be received today (because $1 today could be worth $1.05)

$1(1.05) = $1.05

• Therefore, the present value of $1.05 to be paid in one year (if the annual interest rate is 5%) is $1.

• In general, the PV of $X to be paid in N years is equal to

PV = $X/(1+i)^N

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Income vs. Wealth

• Your wealth is defined and the present value of your lifetime income.

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Income vs. Wealth

• Your wealth is defined and the present value of your lifetime income.

• For example, suppose you expect your annual income to be $50,000 per year for the rest of your life. If the annual interest rate is 3%:Wealth = $50,000 + $50,000/(1.03) + $50,000/(1.03)^2 + ……

= $50,000/(.03) = $1,666,666 (Approx)

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Household Savings

• Without an active capital markets, household consumption is restricted to equal current income (that is, C=Y)

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Household Savings

• Without an active capital markets, household consumption is restricted to equal current income (that is, C=Y)

• With capital markets, the present value of lifetime consumption must equal the present value of lifetime income (assuming all debts are eventually repaid)

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A two period example

• Suppose that your current income is equal to $50,000 and you anticipate next year’s income to be $60,000. The current interest rate is 5%.

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A two period example

• Suppose that your current income is equal to $50,000 and you anticipate next year’s income to be $60,000. The current interest rate is 5%.

• In the absence of capital markets, your consumption stream would be $50,000 this year and $60,000 next year.

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Consumption Possibilities

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Borrowing to increase current consumption

• To increase your current consumption, you could take out a loan. Your current consumption would now be C = $50,000 + Loan

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Borrowing to increase current consumption

• To increase your current consumption, you could take out a loan. Your current consumption would now be

C = $50,000 + Loan• However, you must repay your loan next year.

This implies that

C’= $60,000 – (1.05)Loan

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Borrowing to increase current consumption

• To increase your current consumption, you could take out a loan. Your current consumption would now be

C = $50,000 + Loan

• However, you repay your loan next year. This implies that

C’= $60,000 – (1.05)Loan

• For example, if you take out a $10,000 loan, your current consumption would be $60,000, while your future income would be $60,000 - $10,000(1.05) = $49,500

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Consumption Possibilities

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Borrowing Limits

Note that you need to be able to repay your loan next year. Therefore,

$60,000 > (1.05)Loan

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Borrowing Limits

• Note that you need to be able to repay your loan next year. Therefore,

$60,000 = (1.05)Loan

• Your maximum allowable loan is $60,000/1.05 = $57,143 (this is associated with zero future consumption)

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Borrowing Limits

• Note that you need to be able to repay your loan next year. Therefore, $60,000 = (1.05)LoanYour maximum allowable loan is $60,000/1.05 = $57,143 (this is associated with zero future consumption)Therefore, your maximum current consumption is $107,143

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Consumption Possibilities

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Saving to increase future consumption

• You could increase future consumption by saving some of your income (i.e. a negative loan). Suppose you put $20,000 in the bank, your current consumption is now $30,000.

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Saving to increase future consumption

• You could increase future consumption by saving some of your income (i.e. a negative loan). Suppose you put $20,000 in the bank, your current consumption is now $30,000.

• Next year, your bank account will be worth $20,000(1.05) = $21,000. Therefore, your future consumption will be $81,000

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Consumption Possibilities

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Maximizing future consumption

• Suppose you save your entire income. Your current consumption will be zero, but your future consumption will be

C’ = $60,000 + $50,000(1.05) = $112,500

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Consumption Possibilities

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Suppose that the interest rate rises to 8%

• Note that if you don’t borrow or lend, you are unaffected.

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Suppose that the interest rate rises to 8%

• Note that if you don’t borrow or lend, you are unaffected.

• At higher interest rates, your borrowing limit falls: Loan = $60,000/1.08 = $55,556 (higher interest rates are bad for borrowers)

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Suppose that the interest rate rises to 8%

• Note that if you don’t borrow or lend, you are unaffected.

• At higher interest rates, your borrowing limit falls: Loan = $60,000/1.08 = $55,556 (higher interest rates are bad for borrowers)

• However, if you are saving, you receive more interest: $50,000(1.08) = $54,000 (higher interest rates are good for savers)

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Consumption Possibilities

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Consumption Possibilities

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The interest rate is the relative price of current consumption in terms of future consumption

• When any relative price changes, there are two distinct effects that impact consumer behavior

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The interest rate is the relative price of current consumption in terms of future consumption

• When any relative price changes, there are two distinct effects that impact consumer behavior– The substitution effect: as relative prices change, consumer

typically alter purchases to favor the good that has become cheaper

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The interest rate is the relative price of current consumption in terms of future consumption

• When any relative price changes, there are two distinct effects that impact consumer behavior– The substitution effect: as relative prices change, consumer

typically alter purchases to favor the good that has become cheaper

– Income Effect: Changing prices alter one’s purchasing power. When purchasing power falls/rises, purchases fall/rise

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How does rising interest rates influence savings decisions?

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How does rising interest rates influence savings decisions?

• The substitution effect is unambiguous: as interest rates rise, current consumption becomes more expensive. Therefore, consumers spend less (i.e. save more)

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How does rising interest rates influence savings decisions?

• The substitution effect is unambiguous: as interest rates rise, current consumption becomes more expensive. Therefore, consumers spend less (i.e. save more)

• The income effect depends on your current situation: borrowers experience a negative income effect and therefore would spend less (save more) while savers experience a positive income effect and therefore would spend more (save less)

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Impact of rising interest rates

Borrowers• Substitution effect:

spend less (save more)• Income effect: Spend

less (save more)___________

Net effect: Save More

Savers• Substitution effect:

spend less (save more)• Income effect: spend

more (save less)___________

Net effect: ????

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Aggregate Savings

• At the individual level, we would need to consider income and substitution effects to determine the precise impact of rising/falling interest rates on savings behavior

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Aggregate Savings

• At the individual level, we would need to consider income and substitution effects to determine the precise impact of rising/falling interest rates on savings behavior

• At the aggregate level, new savings is very close to zero (i.e., there are approximately the same number of borrowers as there are lenders

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Aggregate Savings

• At the individual level, we would need to consider income and substitution effects to determine the precise impact of rising/falling interest rates on savings behavior

• At the aggregate level, new savings is very close to zero (i.e., there are approximately the same number of borrowers as there are lenders

• Therefore, the income effects cancel out and higher interest rates have an unambiguous positive effect on savings

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Aggregate Savings

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Again, assume that the interest rate is 5%, consider two individuals

Person A• Current income:

$10,000• Anticipated future

income: $50,000

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Again, assume that the interest rate is 5%, consider two individuals

Person A• Current income:

$10,000• Anticipated future

income: $50,000

Person B• Current Income:

$50,000• Anticipated Future

income: $8,000

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Again, assume that the interest rate is 5%, consider two individuals

Person A• Current income:

$10,000• Anticipated future

income: $50,000

Wealth: $57,619

Person B• Current Income:

$50,000• Anticipated Future

income: $8,000

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Again, assume that the interest rate is 5%, consider two individuals

Person A• Current income:

$10,000• Anticipated future

income: $50,000

Wealth: $57,619

Person B• Current Income:

$50,000• Anticipated Future

income: $8,000

Wealth: $57,619

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Consumption vs. Wealth

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Consumption and Wealth

• With capital markets, consumption is not determined by current income, but by wealth (present value of lifetime income)

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Consumption and Wealth

• With capital markets, consumption is not determined by current income, but by wealth (present value of lifetime income)

• These two individuals, having the same wealth, should choose the same consumption

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Consumption vs. Wealth

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Again, assume that the interest rate is 5%, consider two individuals

• Person A

• Current income: $10,000

• Anticipated future income: $50,000

Wealth: $57,619

Current Spending: $30,000

Person B

• Current Income: $50,000

• Anticipated Future income: $8,000

Wealth: $57,619

Current Spending: $30,000

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Again, assume that the interest rate is 5%, consider two individuals

• Person A

• Current income: $10,000

• Anticipated future income: $50,000

Wealth: $57,619

Current Spending: $30,000

Savings: -$20,000

Person B

• Current Income: $50,000

• Anticipated Future income: $8,000

Wealth: $57,619

Current Spending: $30,000

Savings: $20,000

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Again, assume that the interest rate is 5%, consider two individuals

• Person A

• Current income: $10,000

• Anticipated future income: $50,000

Wealth: $57,619

Current Spending: $30,000

Savings: -$20,000

Future Spending: $29,000

Person B

• Current Income: $50,000

• Anticipated Future income: $8,000

Wealth: $57,619

Current Spending: $30,000

Savings: $20,000

Future Spending: $29,000

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Consumption and Wealth

• With capital markets, consumption is not determined by current income, but by wealth (present value of lifetime income)

• These two individuals, having the same wealth, should choose the same consumption.

• For a given level of wealth, those with high rates of income growth would be expected to be borrowers

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Suppose that economic growth in the US rises. What should happen to aggregate savings?

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Suppose that economic growth in the US rises. What should happen to aggregate savings?

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Technology & Investment Demand

• Recall that an economy has three sources of growth: labor, capital, and technology

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Production Technology

• Recall that an economy has three sources of growth: labor, capital, and technology

• The production function describes the relationship between output and the three

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Production (Holding Employment Fixed)

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Production (Holding Employment Fixed)

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Marginal Product of Capital

• The marginal product of capital is defined as the additional output produced by each additional unit of capital purchased.

• In the previous slide, the first unit of capital generated 25 units of output while the second unit of capital raised total output from 20 to 45

• Therefore, the MPK of the first unit of capital is 25 while the MPK of the second unit of capital is 20

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Diminishing marginal product implies that as the capital stock rises, the marginal product of

additional capital falls

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Marginal Product and Investment Demand

• Recall that investment refers to the purchase of new capital equipment by the private sector

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Marginal Product and Investment Demand

• Recall that investment refers to the purchase of new capital equipment by the private sector

• Firms are profit maximizers and, hence, only take actions that increase firm value (present value of lifetime earnings)

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Marginal Product and Investment Demand

• Recall that investment refers to the purchase of new capital equipment by the private sector

• Firms are profit maximizers and, hence, only take actions that increase firm value (present value of lifetime earnings)

• Therefore a firm will only buy a new piece of capital when the contribution of that capital to firm value is greater that its costP(k) > PV(MPK)

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A Numerical example

• Suppose that the current interest rate is 5% and that the cost of a unit of machinery is $100. Capital is assumed to depreciate at a rate of 10% per year.

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A Numerical example

• Suppose that the current interest rate is 5% and that the cost of a unit of machinery is $100.

• Given the technology from the previous slide, the marginal product of the first unit of capital is $25/yr. Income stream will this capital generate?

• Year 1: $25

Year 2: $25(1-.10) = $22.50

Year 3: $25(1-.10)(1-.10) = $20.25

Year 3: $25(1-.10)(1-.10)(1-.10) = $18.23 …………

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A Numerical example

• What is the present value of this income stream?

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A Numerical example

• What is the present value of this income stream?

PV = $25/(1.05) + $22.50/(1.05)^2 + $20.25/(1.05)^3 + …….

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A Numerical example

• What is the present value of this income stream?

PV = $25/(1.05) + $22.50/(1.05)^2 + $20.25/(1.05)^3 + …….

PV = $25/( i + depreciation ) = $25/(.15) = $167

• Is this a positive NPV project? Yes ( $167 > $100)

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A Numerical example

• What is the present value of this income stream?

PV = $25/(1.05) + $22.50/(1.05)^2 + $20.25/(1.05)^3 + …….

PV = $25/( i + depreciation ) = $25/(.15) = $167

• Is this a positive NPV project? Yes ( $167 > $100)• In fact, solving the above expression tells us that this is a positive NPV

project for any interest rate under

i = (MPK/Pk) – depreciation = ($25/$100) - .10 = .15 = 15%

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Interest rates and Investment

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Interest rates and investment

• Note that once the first unit of capital has been purchased, the second unit of capital only has a marginal product of 20.

• Therefore, for this unit of capital to be a positive PV project, the interest rate must be lower than 20/100 - .10 = .1 = 10%

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Interest rates and Investment

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Interest rates and investment

• Diminishing marginal product of Capital guarantees that the demand for investment is downward sloping (increasing rates of investment require lower interest rates)

• To get the total demand for loans, multiply the investment curve by the price of capital)

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Interest rates and Investment

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Investment Demand

• It is assumed that labor and capital are compliments. That is, when employment rises, the productivity of capital increases as well.

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Investment Demand

• It is assumed that labor and capital are compliments. That is, when employment rises, the productivity of capital increases as well.

• Therefore, as a rise in employment should increase the demand for capital and, hence, the demand for loans

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Investment Demand

• It is assumed that labor and capital are compliments. That is, when employment rises, the productivity of capital increases as well.

• Therefore, as a rise in employment should increase the demand for capital and, hence, the demand for loans

• Further, any technological improvement should also raise the demand for investment

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A rise in investment demand

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A rise in investment demand

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Capital Market Equilibrium

• For now, assume that there is no government and the US is a closed economy

• Add up individual firm’s hiring decisions to get aggregate investment

• Add up individual household decisions to get aggregate savings

• A capital market equilibrium is an interest rate that clears the market (i.e.,savings equals investment)

• Here, i*= 10%, S* = I*= 300

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Example: Post-war Germany

• It is estimated that 20-25% of Germany’s capital stock was destroyed during WWII. How would the German capital market respond to this?

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Example: Post-war Germany

• It is estimated that 20-25% of Germany’s capital stock was destroyed during WWII. How would the German capital market respond to this?

• A lower capital stock decreases increases the productivity of new investment and, thus increases investment demand

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Example: Post-war Germany

• It is estimated that 20-25% of Germany’s capital stock was destroyed during WWII. How would the German capital market respond to this?

• A lower capital stock decreases increases the productivity of new investment and, thus increases investment demand

• The resulting higher equilibrium has a higher interest rate, higher savings and investment 0

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Example:The Bubonic Plague

• The Bubonic Plague, or “Black Death” ravaged Europe in the 1300’s. From 1347-1352, approximately 30% of the population in Europe was killed (25 million). What impact will this have on capital markets?

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Example:The Bubonic Plague

• The Bubonic Plague, or “Black Death” ravaged Europe in the 1300’s. From 1347-1352, approximately 30% of the population in Europe was killed (25 million). What impact will this have on capital markets?

• A decrease in employment lowers the productivity of investment (labor and capital are complements) and, hence, investment demand

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Example:The Bubonic Plague

• The Bubonic Plague, or “Black Death” ravaged Europe in the 1300’s. From 1347-1352, approximately 30% of the population in Europe was killed (25 million). What impact will this have on capital markets?

• A decrease in employment lowers the productivity of investment (labor and capital are complements) and, hence, investment demand

• The result: lower interest rates, savings, and investment

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Temporary vs. Permanent Shocks

• Unlike labor markets, the timing and persistence of productivity shock are important

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Temporary vs. Permanent Shocks

• Unlike labor markets, the timing and persistence of productivity shock are important

• New capital takes time to install. Therefore, productivity improvements must be long lasting to effect investment demand

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Temporary vs. Permanent Shocks

• Unlike labor markets, the timing and persistence of productivity shock are important

• New capital takes time to install. Therefore, productivity improvements must be long lasting to effect investment demand

• A temporary improvement in productivity will increase savings (as consumers smooth this extra income), but have no impact on investment

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Temporary vs. Permanent Shocks

• Unlike labor markets, the timing and persistence of productivity shock are important

• New capital takes time to install. Therefore, productivity improvements must be long lasting to effect investment demand

• On the other hand, a permanent technological improvement will increase investment, but have little impact on savings 0

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