DEFINITION:

FINANCIAL MARKETS are financial institutions through which savers can directly provide funds to borrowers.

DEFINITION: The TERM TO MATURITY of a security is the time from the present until it matures.

Securities are classified as short-term and long-term on the basis of their term to maturity at the time of issue.

DEFINITION:

The FUTURE VALUE is the amount of money in the future that an amount of money today will yield, given prevailing interest rates.

Suppose that interest is paid annually and you put $100 into a bank account paying 5% interest (r) for a year.

The future value of the $100, one year from today is:

FV = $100 (1+.05) = $105.

Where

FV = the future value.

Now let us turn this around.

Suppose you are to receive $105 in 1 year. What would the $105 to be received in 1 year be worth today if you could earn 5% interest on the money if you had it now?

We solve the above equation for this amount and get:

Where PV is the present value.

DEFINITION:

The PRESENT VALUE is the amount of money today that would be needed to produce, using prevailing interest rates, a given future amount of money.

This result can obviously be generalized.

If:

X is the amount of money to be received in 1 year.

r is the rate of interest.

Note that we are still assuming that interest is paid annually.

This can be generalized for X dollars to be paid in n years. We are still assuming interest is paid annually:

where:

n is the number of years in the future when amount X will be paid.

Xn is the amount to be paid in n years.

 

 

This can be generalized to a stream of annual payments of $X for n years.

Note we are still assuming interest is paid annually.

Bonds pay essentially this kind of stream of payments.

Where

C are the coupon payments

M is the maturity or par value

The coupon payment is based on the rate of interest that is stated on the bond, called the coupon rate (or just the coupon), times the par value. For example, a $1,000, 6% bond will pay a coupon payment of $60 each year. It is important to note that this is not the interest rate r in the denominator of the terms. This is set at the time the bond is sold in the primary market and does not change during the term of the bond.

The interest rate (r), on the other hand, is the market interest rate that investors could earn if they invested the money on alternative investments that are comparable to this bond. For example, that have the same degree of risk. Note that this interest rate can change.

The present value is the price at which the bond will sell, so that PV = P, where P is the price of the bond.

If r goes up P goes down, and vice versa.

Yield to Maturity:

DEFINITION:
The YIELD TO MATURITY of a security is that particular interest rate (or rate of discount) that will make the sum of the present values of all of the future payments of the security equal to its purchase price.

This time we know price of bond, P. Need to determine the value of r that makes this equation hold. This is the yield to maturity.

Note that if P increases, r decreases and vice versa.

Where

SH = household sector saving

TN = Net Taxes

TN = T - TR

T = Total Taxes

TR = Transfer Payments

We are assuming

No Retained Earnings

No Depreciation. Therefore no Depreciation Allowances

Therefore no Corporate Saving

[Note: to keep things simple, we are assuming that all businesses are corporations.]

Therefore

SP = SH

Where

SP = Private Saving

 

 

 

SG = TN - G

NS = SP + SG

Where

SG = Government Sector Saving

NS = National Saving

 

 

 

 

 

DEFINITION:

The NOMINAL INTEREST RATE is the interest rate in terms of current dollars.

DEFINITION:

The REAL INTEREST RATE is the interest rate adjusted for inflation (or in terms of constant dollars).

Expected rate of inflation:

The interest rate in Figure L9-3 and in diagrams in Chapter 9 of the text, is the expected real rate of interest.

Note that if = 0

As long as the expected rate of inflation is zero the expected real interest rate and nominal interest rate are the same.

Similarly, as long as the actual rate of inflation is zero, the actual real interest rate and the nominal interest rate are the same.

I = f(, r)

Where

I = planned or desired (physical) investment.

r = the expected rate of return on the investment

Government Sector Deficit =

(G - TN)

When Govt. Sector has deficit:

DLF = I + (G - TN)

DEFINITION:

A STRUCTURAL DEFICIT is what the deficit is when the economy is at potential output,

or

when the economy is not at potential output, what the deficit would be if the economy were at potential output.

SP = g(, DI, ...)

SLF = DLF

Since

SLF = SP

DLF = I + (G - TN)

Substituting, and using simple Algebra, get

SP = I + (G - TN)

SP + (TN - G) = I

SP + SG = I

Conclusion

NS = I

Note that since I is now desired or intended investment, this is an equilibrium condition, not an accounting identity.

CONCLUSION FOR A CLOSED ECONOMY:

AN INCREASE IN THE STRUCTURAL DEFICIT WILL INCREASE THE EXPECTED REAL RATE OF INTEREST AND REDUCE PRIVATE SECTOR INVESTMENT.

EFFECT OF CHANGE IN THE EXPECTED RATE OF INFLATION ON THE NOMINAL RATE OF INTEREST (ON NEW LOANS).

Now have SLF = SP + KI

In the case of perfect capital mobility, the red line becomes horizontal.

KI = k ( ...)

where

= the foreign expected real interest rate

RELATION OF KI AND NET EXPORTS:

Recall from equation 19-1 on page 462:

CA -FA (19-1)

FA is the Balance of Payments on Financial Account.

Therefore:

FA = KI

Substituting, we get:

CA = - KI (19-1a)

CA is the Balance of Payment on Current Account.

If some minor items are omitted:

CA = Balance on Goods and Services = Trade Balance = Net Exports = X - IM.

Substituting in equation 19-1a we get:

(X - IM) - KI (19.1b)

or

KI - (X - IM) (IM - X) (19.1c)

where (IM - X) is the deficit in the trade balance.

From equation 19-1c, if KI = 0, (IM - X) = 0

CONCLUSION FOR OPEN ECONOMY:

AN INCREASE IN THE STRUCTURAL DEFICIT WILL INCREASE THE EXPECTED REAL INTEREST RATE BY LESS THAN IN A CLOSED ECONOMY.

BUT

IT WILL CAUSE A DEFICIT IN THE TRADE BALANCE, OR, IF THERE IS ALREADY A DEFICIT, WILL INCREASE IT.