ECON 330 EQUATIONS UW MADISON

#economics

GDP Deflator

Nominal GDP divided by real GDP, multiplied by 100.

Brokers

agents of investors who match buyers with sellers of securities

Dealers

link buyers and sellers by buying and selling securities at stated prices.

over-the-counter (OTC) market

which dealers at different locations who have an inventory of securities stand ready to buy and sell securities “over the counter” to anyone who comes to them and is will-ing to accept their prices.

money market vs capital market

money market is short term (1 year or less) and capital is longer term debt and equity instruments

What does M2 include that M1 does not?

M2 includes assets that have check-writing features (money market deposit accounts and money market mutual fund shares) and other assets (savings deposits and small-denomination time deposits)

Simple Loan Equation

PV = CF / (1+i)^{n
PV = present value
CF = cash flow / payment
n = number of years
i = interest rate}

yield to maturitty

is the interest rate that equates the present value of cash flow payments received from a debt instrument with its value today.
(Usually i or interest rates in the equations being used)!

bc think, value today = present value of future cash flows.

Fixed-payment loan

LV = FP / (1+i) + FP / (1+i)² … + FP / (1 + i)^{n
LV = loan value amount}
This makes sense because the loan value is the sum of the present values of all future fixed payments.

Coupon Bond

P = C / (1 + i) + C / (1 + i)² … + C / (1 + i)ⁿ + F / (1 + i)ⁿ

^{P = price of bond!
C = yearly coupon payment, which is calculated by the coupon % times the price}

^{F = face value of the bond, because this is repaid at the end}

^{**Follows a similar structure to Fixed-Payment loan, except you will be payed the coupon payment + the original price}

Perpetuity

P_c = C / i_{c
Pc = price of the consol/perpetuity}

_{C = yearly payment}

_{Ic = yield to maturity (expressed as a percent!) which ALSO EQUALS CURRENT YIELD}

Discount Bond

(coupon bond sold at a discount to its face value, does NOT pay back face value)
PV = CF / (1 + i)ⁿ

**similar to simple loans

Current Yield

I_c and is frequently used as an approximation to describe interest rates on long-term bond

simple discount bond interest / yield to maturity

i = F - P / P

Extended rate of return formula

R = C + P_t+1 - P_t all divided by P_t

Rate of capital gain

P_t+1 - P_t / P_t

Simple rate of return formula

R = I_c + g

Nominal interest rate

i = r + π^e
π^{e = expected rate of inflation}

liquidity preference framework

A theory that explains the demand for money and how it influences interest rates, emphasizing the trade-off between holding money and investing.

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DETERMINES INTEREST RATES IN TERMS OF MONEY MARKET NOT BOND MARKET

People store wealth in only two ways: money and bonds, therefore what equation?

Bs + Ms = Bd + Md

One period valuation model for stocks

P₀ = D1 / (1 + K_e) + P₁ / (1 + K_e)
_{D1 = dividend payment}

_{P0 = current price of the stock}

_{Ke = required return on investments in equity (it’s a percentage!)}

_{P1 = price at end of year 1 // predicted sales price of the stock}

Generalized dividend model

P₀ = D₂ / (1 + K_e) + D₂ / (1 + K_e)² + … D_n / (1 + K_e)ⁿ + P_n / (1 + K_e)ⁿ

Gordon Growth Model

P₀ = D_{1 /} (K_e - g)
_{D0 = most recent dividend paid}

_{g = expected constant growth rate in dividends}

_{Ke = required return in equity as a %}