[e]

EC210 ~ MACRO

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[e]

Ec210 MACRO (Tom C)

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<h2 style="margin-top: 0px;">Ec210 MACRO (Tom C)</h2>
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<ol>
<li> <a href="./?body=Home">Home</a> 
<li> <a href="./?body=Handout">Handout</a>
<li> <a href="./?body=Notes">Economic Modelling</a>
<li> <a href="./?body=FirstTerm">First Term Summary</a>
<li> <a 
href="./?body=Definitions">Definitions</a>
<li> <a href="./?body=Models">Models</a>
<li> <a href="./?body=Issues">Issues</a>
<li> <a href="./?body=PDVs">Present Discounted Values</a>
<li> <a href="./?body=Questions">Questions</a>
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[e]

IMPORTANT: This is not official LSE teaching material, use at your own risk!

[e]

Present Discounted Values

Present Discounted Values. Calculating PDVs tells you most of the things about consumption, investment, equity & bond prices that you need to know for this course. The general formula is this:
PDV = Σ_t=1..T[ Π_s=1..t(1+r_s) ]y_t
If the interest rate is constant, then PDV = Σ_t=1..T(1+r)^ty_t
If the interest rate is constant, the payments are constant, and the payments go into the infinite future, then you can use the formula for a geometric sum to get: PDV = y/r.
There's a useful approximation when dealing with interest rates: (1+i)(1+r) ~= 1 + i + r.
Risk premium: Perhaps you don't know exactly what the future payments, or the future interest rates, will be. You can use expected values to calculate a PDV, but you may not want to pay £80 for an investment with an expected PDV of £80, because of the uncertainty about the future payout. In theory you could calculate the present value of an investment in terms of utility, taking into a account uncertainty. In practice, you can say that people use a discount factor above the interest rate to discount risky investments, & you call the difference between the two rates the "risk premium." The historical difference in rates of return between stocks and bonds in the US is around 7%, so people say there's an "equity risk premium," which compensates for the extra riskiness of stocks.
Bond prices. The price of a bond should be equal to the expected discounted value. By comparing the prices of two different bonds which differ in one respect you can infer peoples' expectations, e.g. the expected future interest rate, or the expected inflation rate. For example, from the prices of a one-year and a two-year bond you can infer next year's expected interest rate:
P₁ = 100/(1+r₁)
P₂ = 100/(1+r₁)(1+r₂^e)
Equity. In principle the price of a stock should be equal to the present discounted value of the dividends. The rate of dividends always varies, so you will generally discount with a risk premium.
Consumption. If a person has access to a credit market (i.e., they can save and borrow at the interest rate r) then the PDV of their income should equal the PDV of their wealth.
Investment.

<h1>Present Discounted Values</h1><ul>

<li> Present Discounted Values. Calculating PDVs tells you most of the things about consumption, investment, equity & bond prices that you need to know for this course. The general formula is this: 
 PDV = &Sigma;t=1..T[ &Pi;s=1..t(1+rs) ]yt

<li> If the interest rate is constant, then PDV = &Sigma;t=1..T(1+r)tyt

<li> If the interest rate is constant, the payments are constant, and the payments go into the infinite future, then you can use the formula for a geometric sum to get: PDV = y/r.

<li> There's a useful approximation when dealing with interest rates: (1+i)(1+r) ~= 1 + i + r.

<li> Risk premium: Perhaps you don't know exactly what the future payments, or the future interest rates, will be. You can use expected values to calculate a PDV, but you may not want to pay &pound;80 for an investment with an expected PDV of &pound;80, because of the uncertainty about the future payout. In theory you could calculate the present value of an investment in terms of utility, taking into a account uncertainty. In practice, you can say that people use a discount factor above the interest rate to discount risky investments, & you call the difference between the two rates the "risk premium." The historical difference in rates of return between stocks and bonds in the US is around 7%, so people say there's an "equity risk premium," which compensates for the extra riskiness of stocks.

<li> Bond prices. The price of a bond should be equal to the expected discounted value. By comparing the prices of two different bonds which differ in one respect you can infer peoples' expectations, e.g. the expected future interest rate, or the expected inflation rate. For example, from the prices of a one-year and a two-year bond you can infer next year's expected interest rate: 
 P1 = 100/(1+r1) 
 P2 = 100/(1+r1)(1+r2e)

<li> Equity. In principle the price of a stock should be equal to the present discounted value of the dividends. The rate of dividends always varies, so you will generally discount with a risk premium.

<li> Consumption. If a person has access to a credit market (i.e., they can save and borrow at the interest rate r) then the PDV of their income should equal the PDV of their wealth.

<li> Investment.

</ul>

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