The Stock Market, the Theory of Rational Expectationsand the Effi cient Market Hypothesis

Money and Banking

Cesar E. TamayoDepartment of Economics, Rutgers University

July 25, 2011

C.E. Tamayo () Econ - 301 July 25, 2011 1 / 20

Revisiting risk premiumProgram

ReCap

The stock market: recent trends

The valuation of stocks

How the market sets stock prices

The theory of rational expectations

The effi cient market hypothesis

C.E. Tamayo () Econ - 301 July 25, 2011 2 / 20

The stock market recent trends

Suppose that when you turned 1y/o your wealthy uncle gave you abirthday present: a $2,500 investment in the NYSE. How much wouldyou have today?

(a) $1,544

(b) $3,000

(c) $5,567

(d) $9,416

Correct answer: $9,416

C.E. Tamayo () Econ - 301 July 25, 2011 3 / 20

The stock market recent trends

Suppose that when you turned 1y/o your wealthy uncle gave you abirthday present: a $2,500 investment in the NYSE. How much wouldyou have today?

(a) $1,544

(b) $3,000

(c) $5,567

(d) $9,416

Correct answer: $9,416

C.E. Tamayo () Econ - 301 July 25, 2011 3 / 20

The stock market recent trends

Suppose that when you turned 1y/o your wealthy uncle gave you abirthday present: a $2,500 investment in the NYSE. How much wouldyou have today?

(a) $1,544

(b) $3,000

(c) $5,567

(d) $9,416

Correct answer: $9,416

C.E. Tamayo () Econ - 301 July 25, 2011 3 / 20

The stock market recent trends

Suppose that when you turned 1y/o your wealthy uncle gave you abirthday present: a $2,500 investment in the NYSE. How much wouldyou have today?

(a) $1,544

(b) $3,000

(c) $5,567

(d) $9,416

Correct answer: $9,416

C.E. Tamayo () Econ - 301 July 25, 2011 3 / 20

The stock market recent trends

Suppose that when you turned 1y/o your wealthy uncle gave you abirthday present: a $2,500 investment in the NYSE. How much wouldyou have today?

(a) $1,544

(b) $3,000

(c) $5,567

(d) $9,416

Correct answer: $9,416

C.E. Tamayo () Econ - 301 July 25, 2011 3 / 20

The stock market recent trends

Suppose that when you turned 1y/o your wealthy uncle gave you abirthday present: a $2,500 investment in the NYSE. How much wouldyou have today?

(a) $1,544

(b) $3,000

(c) $5,567

(d) $9,416

Correct answer: $9,416

C.E. Tamayo () Econ - 301 July 25, 2011 3 / 20

The stock market recent trends: S&P 500 1990-2011

C.E. Tamayo () Econ - 301 July 25, 2011 4 / 20

The valuation of stocks

First some terminology

Stockholder. Residual Claimant.

Next, what is the "right" price of a stock? Use our GOF, the PVconcept:

PV =CF

(1+ i)n

Where:

PV = price of stock today

CF = dividends and/or sales price

i = return of your investment

n = periods you hold the stock

C.E. Tamayo () Econ - 301 July 25, 2011 5 / 20

The valuation of stocks

First some terminology

Stockholder. Residual Claimant.

Next, what is the "right" price of a stock? Use our GOF, the PVconcept:

PV =CF

(1+ i)n

Where:

PV = price of stock today

CF = dividends and/or sales price

i = return of your investment

n = periods you hold the stock

C.E. Tamayo () Econ - 301 July 25, 2011 5 / 20

The valuation of stocks

First some terminology

Stockholder. Residual Claimant.

Next, what is the "right" price of a stock? Use our GOF, the PVconcept:

PV =CF

(1+ i)n

Where:

PV = price of stock today

CF = dividends and/or sales price

i = return of your investment

n = periods you hold the stock

C.E. Tamayo () Econ - 301 July 25, 2011 5 / 20

The valuation of stocks

First some terminology

Stockholder. Residual Claimant.

Next, what is the "right" price of a stock? Use our GOF, the PVconcept:

PV =CF

(1+ i)n

Where:

PV = price of stock today

CF = dividends and/or sales price

i = return of your investment

n = periods you hold the stock

C.E. Tamayo () Econ - 301 July 25, 2011 5 / 20

The valuation of stocks: generalized dividend model

Suppose that you buy a stock at price P0, which pays dividend perperiod D1 and at the end of one period you sell it for P1. Denoting keas your expected return from this investment, we can use the PVformula with only slight adjustments in notation:

P0 =D11+ ke

+P1

1+ ke

Or, we can generalize this framework as:

P0 =D11+ ke

+D2

(1+ ke )2 + ...+

Dn(1+ ke )

n +Pn

(1+ ke )n

If you hold the stock forever the last term will not be there. Of courseyou cannot hold it forever forever. But if the selling period is farenough in the future, we know that:

limn→∞

P1(1+ ke )

n = 0 w/e (1+ ke ) > 1

C.E. Tamayo () Econ - 301 July 25, 2011 6 / 20

The valuation of stocks: generalized dividend model

Suppose that you buy a stock at price P0, which pays dividend perperiod D1 and at the end of one period you sell it for P1. Denoting keas your expected return from this investment, we can use the PVformula with only slight adjustments in notation:

P0 =D11+ ke

+P1

1+ keOr, we can generalize this framework as:

P0 =D11+ ke

+D2

(1+ ke )2 + ...+

Dn(1+ ke )

n +Pn

(1+ ke )n

If you hold the stock forever the last term will not be there. Of courseyou cannot hold it forever forever. But if the selling period is farenough in the future, we know that:

limn→∞

P1(1+ ke )

n = 0 w/e (1+ ke ) > 1

C.E. Tamayo () Econ - 301 July 25, 2011 6 / 20

The valuation of stocks: generalized dividend model

Suppose that you buy a stock at price P0, which pays dividend perperiod D1 and at the end of one period you sell it for P1. Denoting keas your expected return from this investment, we can use the PVformula with only slight adjustments in notation:

P0 =D11+ ke

+P1

1+ keOr, we can generalize this framework as:

P0 =D11+ ke

+D2

(1+ ke )2 + ...+

Dn(1+ ke )

n +Pn

(1+ ke )n

If you hold the stock forever the last term will not be there. Of courseyou cannot hold it forever forever. But if the selling period is farenough in the future, we know that:

limn→∞

P1(1+ ke )

n = 0 w/e (1+ ke ) > 1

C.E. Tamayo () Econ - 301 July 25, 2011 6 / 20

The valuation of stocks: generalized dividend model

So that we can ignore the last term and end up with:

P0 =∞

∑t=0

Dt(1+ ke )

t (1)

Now, we know that these quantities mean (P0,Dt , ke ,Pt) but wheredo they come from?

We saw that if the sale takes place far in the future Pt will not matter.

ke will usually be a measure of the opportunity cost, say, the interestrate payed by bonds plus some premia.

On the other hand, Dt can be estimated and for the short term it canbe announced by the issuer.

But even if we knew Dt for all t, this is an infinite sum with nocommon term (can’t use geometric series). So...

C.E. Tamayo () Econ - 301 July 25, 2011 7 / 20

The valuation of stocks: generalized dividend model

So that we can ignore the last term and end up with:

P0 =∞

∑t=0

Dt(1+ ke )

t (1)

Now, we know that these quantities mean (P0,Dt , ke ,Pt) but wheredo they come from?

We saw that if the sale takes place far in the future Pt will not matter.

ke will usually be a measure of the opportunity cost, say, the interestrate payed by bonds plus some premia.

On the other hand, Dt can be estimated and for the short term it canbe announced by the issuer.

But even if we knew Dt for all t, this is an infinite sum with nocommon term (can’t use geometric series). So...

C.E. Tamayo () Econ - 301 July 25, 2011 7 / 20

The valuation of stocks: generalized dividend model

So that we can ignore the last term and end up with:

P0 =∞

∑t=0

Dt(1+ ke )

t (1)

Now, we know that these quantities mean (P0,Dt , ke ,Pt) but wheredo they come from?

We saw that if the sale takes place far in the future Pt will not matter.

ke will usually be a measure of the opportunity cost, say, the interestrate payed by bonds plus some premia.

On the other hand, Dt can be estimated and for the short term it canbe announced by the issuer.

But even if we knew Dt for all t, this is an infinite sum with nocommon term (can’t use geometric series). So...

C.E. Tamayo () Econ - 301 July 25, 2011 7 / 20

The valuation of stocks: generalized dividend model

So that we can ignore the last term and end up with:

P0 =∞

∑t=0

Dt(1+ ke )

t (1)

Now, we know that these quantities mean (P0,Dt , ke ,Pt) but wheredo they come from?

We saw that if the sale takes place far in the future Pt will not matter.

ke will usually be a measure of the opportunity cost, say, the interestrate payed by bonds plus some premia.

On the other hand, Dt can be estimated and for the short term it canbe announced by the issuer.

But even if we knew Dt for all t, this is an infinite sum with nocommon term (can’t use geometric series). So...

C.E. Tamayo () Econ - 301 July 25, 2011 7 / 20

The valuation of stocks: generalized dividend model

So that we can ignore the last term and end up with:

P0 =∞

∑t=0

Dt(1+ ke )

t (1)

Now, we know that these quantities mean (P0,Dt , ke ,Pt) but wheredo they come from?

We saw that if the sale takes place far in the future Pt will not matter.

ke will usually be a measure of the opportunity cost, say, the interestrate payed by bonds plus some premia.

On the other hand, Dt can be estimated and for the short term it canbe announced by the issuer.

But even if we knew Dt for all t, this is an infinite sum with nocommon term (can’t use geometric series). So...

C.E. Tamayo () Econ - 301 July 25, 2011 7 / 20

The valuation of stocks: generalized dividend model

So that we can ignore the last term and end up with:

P0 =∞

∑t=0

Dt(1+ ke )

t (1)

Now, we know that these quantities mean (P0,Dt , ke ,Pt) but wheredo they come from?

We saw that if the sale takes place far in the future Pt will not matter.

ke will usually be a measure of the opportunity cost, say, the interestrate payed by bonds plus some premia.

On the other hand, Dt can be estimated and for the short term it canbe announced by the issuer.

But even if we knew Dt for all t, this is an infinite sum with nocommon term (can’t use geometric series). So...

C.E. Tamayo () Econ - 301 July 25, 2011 7 / 20

The valuation of stocks: Gordon growth model

Simplifying assumption: dividends grow at a constant rate, g .

So, if D0 is the most recent dividend payed, equation (1) can bewritten:

P0 =D0 × (1+ g)1+ ke

+D0 × (1+ g)2

(1+ ke )2 + ...+

D0 × (1+ g)∞

(1+ ke )∞

And if we assume that ke > g we can rewrite as:

P0 =D0 × (1+ g)ke − g

Naturally this valuation model depends crucially upon the twosimplifying assumptions.

C.E. Tamayo () Econ - 301 July 25, 2011 8 / 20

The valuation of stocks: Gordon growth model

Simplifying assumption: dividends grow at a constant rate, g .

So, if D0 is the most recent dividend payed, equation (1) can bewritten:

P0 =D0 × (1+ g)1+ ke

+D0 × (1+ g)2

(1+ ke )2 + ...+

D0 × (1+ g)∞

(1+ ke )∞

And if we assume that ke > g we can rewrite as:

P0 =D0 × (1+ g)ke − g

Naturally this valuation model depends crucially upon the twosimplifying assumptions.

C.E. Tamayo () Econ - 301 July 25, 2011 8 / 20

The valuation of stocks: Gordon growth model

Simplifying assumption: dividends grow at a constant rate, g .

So, if D0 is the most recent dividend payed, equation (1) can bewritten:

P0 =D0 × (1+ g)1+ ke

+D0 × (1+ g)2

(1+ ke )2 + ...+

D0 × (1+ g)∞

(1+ ke )∞

And if we assume that ke > g we can rewrite as:

P0 =D0 × (1+ g)ke − g

Naturally this valuation model depends crucially upon the twosimplifying assumptions.

C.E. Tamayo () Econ - 301 July 25, 2011 8 / 20

The valuation of stocks: Gordon growth model

Simplifying assumption: dividends grow at a constant rate, g .

So, if D0 is the most recent dividend payed, equation (1) can bewritten:

P0 =D0 × (1+ g)1+ ke

+D0 × (1+ g)2

(1+ ke )2 + ...+

D0 × (1+ g)∞

(1+ ke )∞

And if we assume that ke > g we can rewrite as:

P0 =D0 × (1+ g)ke − g

Naturally this valuation model depends crucially upon the twosimplifying assumptions.

C.E. Tamayo () Econ - 301 July 25, 2011 8 / 20

How the market sets stock prices

C.E. Tamayo () Econ - 301 July 25, 2011 9 / 20

How the market sets stock prices

C.E. Tamayo () Econ - 301 July 25, 2011 10 / 20

How the market sets stock prices

C.E. Tamayo () Econ - 301 July 25, 2011 11 / 20

How the market sets stock prices

An electronic auction.

Potential buyers bid while potential sellers ask in an electronictransactional system.

Note: the price is set by the buyer willing to pay the highest price.

BUT: it is not necessarily the highest price this buyer would pay.

Therefore, the asset goes to whoever values it more.

Thus, valuation is key; information and accurate estimates about Dt(or g) are critical.

Also, ke is crucial; investors requiring high ke will have lower bids(they may dislike risk more than others)

C.E. Tamayo () Econ - 301 July 25, 2011 12 / 20

How the market sets stock prices

An electronic auction.

Potential buyers bid while potential sellers ask in an electronictransactional system.

Note: the price is set by the buyer willing to pay the highest price.

BUT: it is not necessarily the highest price this buyer would pay.

Therefore, the asset goes to whoever values it more.

Thus, valuation is key; information and accurate estimates about Dt(or g) are critical.

Also, ke is crucial; investors requiring high ke will have lower bids(they may dislike risk more than others)

C.E. Tamayo () Econ - 301 July 25, 2011 12 / 20

How the market sets stock prices

An electronic auction.

Potential buyers bid while potential sellers ask in an electronictransactional system.

Note: the price is set by the buyer willing to pay the highest price.

BUT: it is not necessarily the highest price this buyer would pay.

Therefore, the asset goes to whoever values it more.

Thus, valuation is key; information and accurate estimates about Dt(or g) are critical.

Also, ke is crucial; investors requiring high ke will have lower bids(they may dislike risk more than others)

C.E. Tamayo () Econ - 301 July 25, 2011 12 / 20

How the market sets stock prices

An electronic auction.

Potential buyers bid while potential sellers ask in an electronictransactional system.

Note: the price is set by the buyer willing to pay the highest price.

BUT: it is not necessarily the highest price this buyer would pay.

Therefore, the asset goes to whoever values it more.

Thus, valuation is key; information and accurate estimates about Dt(or g) are critical.

Also, ke is crucial; investors requiring high ke will have lower bids(they may dislike risk more than others)

C.E. Tamayo () Econ - 301 July 25, 2011 12 / 20

How the market sets stock prices

An electronic auction.

Potential buyers bid while potential sellers ask in an electronictransactional system.

Note: the price is set by the buyer willing to pay the highest price.

BUT: it is not necessarily the highest price this buyer would pay.

Therefore, the asset goes to whoever values it more.

Thus, valuation is key; information and accurate estimates about Dt(or g) are critical.

Also, ke is crucial; investors requiring high ke will have lower bids(they may dislike risk more than others)

C.E. Tamayo () Econ - 301 July 25, 2011 12 / 20

How the market sets stock prices

An electronic auction.

Potential buyers bid while potential sellers ask in an electronictransactional system.

Note: the price is set by the buyer willing to pay the highest price.

BUT: it is not necessarily the highest price this buyer would pay.

Therefore, the asset goes to whoever values it more.

Thus, valuation is key; information and accurate estimates about Dt(or g) are critical.

Also, ke is crucial; investors requiring high ke will have lower bids(they may dislike risk more than others)

C.E. Tamayo () Econ - 301 July 25, 2011 12 / 20

How the market sets stock prices

An electronic auction.

Potential buyers bid while potential sellers ask in an electronictransactional system.

Note: the price is set by the buyer willing to pay the highest price.

BUT: it is not necessarily the highest price this buyer would pay.

Therefore, the asset goes to whoever values it more.

Thus, valuation is key; information and accurate estimates about Dt(or g) are critical.

Also, ke is crucial; investors requiring high ke will have lower bids(they may dislike risk more than others)

C.E. Tamayo () Econ - 301 July 25, 2011 12 / 20

How the market sets stock prices: monetary policy andstocks

Sppose that the Fed were to increase the money supply or reduceinterest rates (recall our analysis of the money market).

First:↑ M ⇒↓ i ⇒↓ ke ⇒↑ P0

So that if you currently hold stocks, you are very happy!

Second:↑ M ⇒↓ i ⇒↑ Y ⇒↑ g ⇒↑ P0

So now you’re even happier!

Naturally this last effect is subject to the caveats we discussed before(recall Keynes vs Friedman).

C.E. Tamayo () Econ - 301 July 25, 2011 13 / 20

How the market sets stock prices: monetary policy andstocks

Sppose that the Fed were to increase the money supply or reduceinterest rates (recall our analysis of the money market).

First:↑ M ⇒↓ i ⇒↓ ke ⇒↑ P0

So that if you currently hold stocks, you are very happy!

Second:↑ M ⇒↓ i ⇒↑ Y ⇒↑ g ⇒↑ P0

So now you’re even happier!

Naturally this last effect is subject to the caveats we discussed before(recall Keynes vs Friedman).

C.E. Tamayo () Econ - 301 July 25, 2011 13 / 20

How the market sets stock prices: monetary policy andstocks

Sppose that the Fed were to increase the money supply or reduceinterest rates (recall our analysis of the money market).

First:↑ M ⇒↓ i ⇒↓ ke ⇒↑ P0

So that if you currently hold stocks, you are very happy!

Second:↑ M ⇒↓ i ⇒↑ Y ⇒↑ g ⇒↑ P0

So now you’re even happier!

Naturally this last effect is subject to the caveats we discussed before(recall Keynes vs Friedman).

C.E. Tamayo () Econ - 301 July 25, 2011 13 / 20

How the market sets stock prices: monetary policy andstocks

Sppose that the Fed were to increase the money supply or reduceinterest rates (recall our analysis of the money market).

First:↑ M ⇒↓ i ⇒↓ ke ⇒↑ P0

So that if you currently hold stocks, you are very happy!

Second:↑ M ⇒↓ i ⇒↑ Y ⇒↑ g ⇒↑ P0

So now you’re even happier!

Naturally this last effect is subject to the caveats we discussed before(recall Keynes vs Friedman).

C.E. Tamayo () Econ - 301 July 25, 2011 13 / 20

How the market sets stock prices: monetary policy andstocks

Sppose that the Fed were to increase the money supply or reduceinterest rates (recall our analysis of the money market).

First:↑ M ⇒↓ i ⇒↓ ke ⇒↑ P0

So that if you currently hold stocks, you are very happy!

Second:↑ M ⇒↓ i ⇒↑ Y ⇒↑ g ⇒↑ P0

So now you’re even happier!

Naturally this last effect is subject to the caveats we discussed before(recall Keynes vs Friedman).

C.E. Tamayo () Econ - 301 July 25, 2011 13 / 20

How the market sets stock prices: monetary policy andstocks

Sppose that the Fed were to increase the money supply or reduceinterest rates (recall our analysis of the money market).

First:↑ M ⇒↓ i ⇒↓ ke ⇒↑ P0

So that if you currently hold stocks, you are very happy!

Second:↑ M ⇒↓ i ⇒↑ Y ⇒↑ g ⇒↑ P0

So now you’re even happier!

Naturally this last effect is subject to the caveats we discussed before(recall Keynes vs Friedman).

C.E. Tamayo () Econ - 301 July 25, 2011 13 / 20

The role of expectations; rational vs adaptive expectations

Because we don’t know Dt , ke or g , what we expect of them in thefuture becomes critical.

Adaptive expectations: future values of a certain variable areexpected to be some average of its past values.

Technical appendix:

xet = (1− ρ)∞

∑j=0

ρjxt−j

Note that because of the long history dependence, changes in thevariable’s value only affect expectations marginally.

C.E. Tamayo () Econ - 301 July 25, 2011 14 / 20

The role of expectations; rational vs adaptive expectations

Because we don’t know Dt , ke or g , what we expect of them in thefuture becomes critical.

Adaptive expectations: future values of a certain variable areexpected to be some average of its past values.

Technical appendix:

xet = (1− ρ)∞

∑j=0

ρjxt−j

Note that because of the long history dependence, changes in thevariable’s value only affect expectations marginally.

C.E. Tamayo () Econ - 301 July 25, 2011 14 / 20

The role of expectations; rational vs adaptive expectations

Because we don’t know Dt , ke or g , what we expect of them in thefuture becomes critical.

Adaptive expectations: future values of a certain variable areexpected to be some average of its past values.

Technical appendix:

xet = (1− ρ)∞

∑j=0

ρjxt−j

Note that because of the long history dependence, changes in thevariable’s value only affect expectations marginally.

C.E. Tamayo () Econ - 301 July 25, 2011 14 / 20

The role of expectations; rational vs adaptive expectations

Because we don’t know Dt , ke or g , what we expect of them in thefuture becomes critical.

Adaptive expectations: future values of a certain variable areexpected to be some average of its past values.

Technical appendix:

xet = (1− ρ)∞

∑j=0

ρjxt−j

Note that because of the long history dependence, changes in thevariable’s value only affect expectations marginally.

C.E. Tamayo () Econ - 301 July 25, 2011 14 / 20

The role of expectations; rational vs adaptive expectations

Rational expectations: expectations will be identical to optimalforecasts using all available information:

Xe = Xof

Technical appendix: if X is the a random variable of interest andX e = E [X ] is the mathematical expectation of X , the theory REimplies that the forectast error of expectations will, on average, bezero:

1T

T

∑t=0(Et [Xt+1]− Xt+1) = 0

and cannot be predicted in advance.Even though a rational expectation equals the optimal forecast usingall available information, a prediction based on it may not always beperfectly accurate

It takes too much effort to make the expectation the best guess possibleBest guess will not be accurate because predictor is unaware of somerelevant information

However, rational expectations 6= perfect foresight.

C.E. Tamayo () Econ - 301 July 25, 2011 15 / 20

The role of expectations; rational vs adaptive expectations

Rational expectations: expectations will be identical to optimalforecasts using all available information:

Xe = Xof

Technical appendix: if X is the a random variable of interest andX e = E [X ] is the mathematical expectation of X , the theory REimplies that the forectast error of expectations will, on average, bezero:

1T

T

∑t=0(Et [Xt+1]− Xt+1) = 0

and cannot be predicted in advance.

Even though a rational expectation equals the optimal forecast usingall available information, a prediction based on it may not always beperfectly accurate

It takes too much effort to make the expectation the best guess possibleBest guess will not be accurate because predictor is unaware of somerelevant information

However, rational expectations 6= perfect foresight.

C.E. Tamayo () Econ - 301 July 25, 2011 15 / 20

The role of expectations; rational vs adaptive expectations

Rational expectations: expectations will be identical to optimalforecasts using all available information:

Xe = Xof

Technical appendix: if X is the a random variable of interest andX e = E [X ] is the mathematical expectation of X , the theory REimplies that the forectast error of expectations will, on average, bezero:

1T

T

∑t=0(Et [Xt+1]− Xt+1) = 0

and cannot be predicted in advance.Even though a rational expectation equals the optimal forecast usingall available information, a prediction based on it may not always beperfectly accurate

It takes too much effort to make the expectation the best guess possibleBest guess will not be accurate because predictor is unaware of somerelevant information

However, rational expectations 6= perfect foresight.

C.E. Tamayo () Econ - 301 July 25, 2011 15 / 20

The role of expectations; rational vs adaptive expectations

Rational expectations: expectations will be identical to optimalforecasts using all available information:

Xe = Xof

Technical appendix: if X is the a random variable of interest andX e = E [X ] is the mathematical expectation of X , the theory REimplies that the forectast error of expectations will, on average, bezero:

1T

T

∑t=0(Et [Xt+1]− Xt+1) = 0

and cannot be predicted in advance.Even though a rational expectation equals the optimal forecast usingall available information, a prediction based on it may not always beperfectly accurate

It takes too much effort to make the expectation the best guess possible

Best guess will not be accurate because predictor is unaware of somerelevant information

However, rational expectations 6= perfect foresight.

C.E. Tamayo () Econ - 301 July 25, 2011 15 / 20

The role of expectations; rational vs adaptive expectations

Rational expectations: expectations will be identical to optimalforecasts using all available information:

Xe = Xof

Technical appendix: if X is the a random variable of interest andX e = E [X ] is the mathematical expectation of X , the theory REimplies that the forectast error of expectations will, on average, bezero:

1T

T

∑t=0(Et [Xt+1]− Xt+1) = 0

and cannot be predicted in advance.Even though a rational expectation equals the optimal forecast usingall available information, a prediction based on it may not always beperfectly accurate

It takes too much effort to make the expectation the best guess possibleBest guess will not be accurate because predictor is unaware of somerelevant information

However, rational expectations 6= perfect foresight.

C.E. Tamayo () Econ - 301 July 25, 2011 15 / 20

The role of expectations; rational vs adaptive expectations

Rational expectations: expectations will be identical to optimalforecasts using all available information:

Xe = Xof

Technical appendix: if X is the a random variable of interest andX e = E [X ] is the mathematical expectation of X , the theory REimplies that the forectast error of expectations will, on average, bezero:

1T

T

∑t=0(Et [Xt+1]− Xt+1) = 0

and cannot be predicted in advance.Even though a rational expectation equals the optimal forecast usingall available information, a prediction based on it may not always beperfectly accurate

It takes too much effort to make the expectation the best guess possibleBest guess will not be accurate because predictor is unaware of somerelevant information

However, rational expectations 6= perfect foresight.C.E. Tamayo () Econ - 301 July 25, 2011 15 / 20

The role of expectations; rational vs adaptive xpectations

ExampleSuppose that you are back in Sep. 2007. You want to know if it is a goodidea to buy stocks issued by Lehman Bros. If you were a ’adaptive’expectations person you would predict something like an annual growth ofxx% for the company in the coming years (2008-). However, if you formyour expectations rationally, you would consider the additional informationavailable to you; a major shock just hit US financial markets through thedefault of many ’subprime”mortgages. Not only the financial institutionsthat lent the money are in trouble, but also those who bought largeamounts of ’securitized’debt obligations (CDOs, MDOs) including yourtarget company, Lehman Bros. Thus, if you behave ’rationally’, yourfuture expectations about g will be dramatically different than if youbehave ’adaptively’

C.E. Tamayo () Econ - 301 July 25, 2011 16 / 20

Rational expectations and the effi cient market hypothesis

Rational expectations are used in all areas of decision making.

When applied to financial markets, the result is the effi cient marketshypothesis:

Theorem (effi cient markets hypothesis)In an effi cient market, a security’s current price reflects all currentlyavailable information

Recall our formula for obtaining the rate of return from t to t + 1:

R =CFPt︸︷︷︸

cash pymnts

+Pt+1 − Pt

Pt︸ ︷︷ ︸capital gain

Suppose that CF and Pt+1 are uncertain, then applying the rationalexpectations theory:

Re = Rof =CF of

Pt+Poft+1 − Pt

Pt

C.E. Tamayo () Econ - 301 July 25, 2011 17 / 20

Rational expectations and the effi cient market hypothesis

Rational expectations are used in all areas of decision making.When applied to financial markets, the result is the effi cient marketshypothesis:

Theorem (effi cient markets hypothesis)In an effi cient market, a security’s current price reflects all currentlyavailable information

Recall our formula for obtaining the rate of return from t to t + 1:

R =CFPt︸︷︷︸

cash pymnts

+Pt+1 − Pt

Pt︸ ︷︷ ︸capital gain

Suppose that CF and Pt+1 are uncertain, then applying the rationalexpectations theory:

Re = Rof =CF of

Pt+Poft+1 − Pt

Pt

C.E. Tamayo () Econ - 301 July 25, 2011 17 / 20

Rational expectations and the effi cient market hypothesis

Rational expectations are used in all areas of decision making.When applied to financial markets, the result is the effi cient marketshypothesis:

Theorem (effi cient markets hypothesis)In an effi cient market, a security’s current price reflects all currentlyavailable information

Recall our formula for obtaining the rate of return from t to t + 1:

R =CFPt︸︷︷︸

cash pymnts

+Pt+1 − Pt

Pt︸ ︷︷ ︸capital gain

Suppose that CF and Pt+1 are uncertain, then applying the rationalexpectations theory:

Re = Rof =CF of

Pt+Poft+1 − Pt

Pt

C.E. Tamayo () Econ - 301 July 25, 2011 17 / 20

Rational expectations and the effi cient market hypothesis

Rational expectations are used in all areas of decision making.When applied to financial markets, the result is the effi cient marketshypothesis:

Theorem (effi cient markets hypothesis)In an effi cient market, a security’s current price reflects all currentlyavailable information

Recall our formula for obtaining the rate of return from t to t + 1:

R =CFPt︸︷︷︸

cash pymnts

+Pt+1 − Pt

Pt︸ ︷︷ ︸capital gain

Suppose that CF and Pt+1 are uncertain, then applying the rationalexpectations theory:

Re = Rof =CF of

Pt+Poft+1 − Pt

Pt

C.E. Tamayo () Econ - 301 July 25, 2011 17 / 20

Rational expectations and the effi cient market hypothesis

Rational expectations are used in all areas of decision making.When applied to financial markets, the result is the effi cient marketshypothesis:

Theorem (effi cient markets hypothesis)In an effi cient market, a security’s current price reflects all currentlyavailable information

Recall our formula for obtaining the rate of return from t to t + 1:

R =CFPt︸︷︷︸

cash pymnts

+Pt+1 − Pt

Pt︸ ︷︷ ︸capital gain

Suppose that CF and Pt+1 are uncertain, then applying the rationalexpectations theory:

Re = Rof =CF of

Pt+Poft+1 − Pt

PtC.E. Tamayo () Econ - 301 July 25, 2011 17 / 20

Rational expectations and the effi cient market hypothesis

But can we observe Re? This is based on the expectations.of eachmarket participant...

But recall our analysis of the bonds and money markets; interest ratesexhibit a tendency to converge towards equilibrium: RE .

Thus, we can use:Re = RE ⇒ RE = Rof

Does the EMH make sense?

Consider arbitrage: unexploited profit opportunities. Suppose that forsome asset RE < Rof , so that you (and probably everyone else)predict that in the future that investment on such asset will yield ahigher return than the current equilibrium return.

Then you (and probably many more) will buy such asset driving up itsprice so, the expected return on this asset falls until again RE = Rof .

Note: if RE 6= Rof somebody must be ill-informed

C.E. Tamayo () Econ - 301 July 25, 2011 18 / 20

Rational expectations and the effi cient market hypothesis

But can we observe Re? This is based on the expectations.of eachmarket participant...

But recall our analysis of the bonds and money markets; interest ratesexhibit a tendency to converge towards equilibrium: RE .

Thus, we can use:Re = RE ⇒ RE = Rof

Does the EMH make sense?

Consider arbitrage: unexploited profit opportunities. Suppose that forsome asset RE < Rof , so that you (and probably everyone else)predict that in the future that investment on such asset will yield ahigher return than the current equilibrium return.

Then you (and probably many more) will buy such asset driving up itsprice so, the expected return on this asset falls until again RE = Rof .

Note: if RE 6= Rof somebody must be ill-informed

C.E. Tamayo () Econ - 301 July 25, 2011 18 / 20

Rational expectations and the effi cient market hypothesis

But can we observe Re? This is based on the expectations.of eachmarket participant...

But recall our analysis of the bonds and money markets; interest ratesexhibit a tendency to converge towards equilibrium: RE .

Thus, we can use:Re = RE ⇒ RE = Rof

Does the EMH make sense?

Consider arbitrage: unexploited profit opportunities. Suppose that forsome asset RE < Rof , so that you (and probably everyone else)predict that in the future that investment on such asset will yield ahigher return than the current equilibrium return.

Then you (and probably many more) will buy such asset driving up itsprice so, the expected return on this asset falls until again RE = Rof .

Note: if RE 6= Rof somebody must be ill-informed

C.E. Tamayo () Econ - 301 July 25, 2011 18 / 20

Rational expectations and the effi cient market hypothesis

But can we observe Re? This is based on the expectations.of eachmarket participant...

But recall our analysis of the bonds and money markets; interest ratesexhibit a tendency to converge towards equilibrium: RE .

Thus, we can use:Re = RE ⇒ RE = Rof

Does the EMH make sense?

Consider arbitrage: unexploited profit opportunities. Suppose that forsome asset RE < Rof , so that you (and probably everyone else)predict that in the future that investment on such asset will yield ahigher return than the current equilibrium return.

Then you (and probably many more) will buy such asset driving up itsprice so, the expected return on this asset falls until again RE = Rof .

Note: if RE 6= Rof somebody must be ill-informed

C.E. Tamayo () Econ - 301 July 25, 2011 18 / 20

Rational expectations and the effi cient market hypothesis

But can we observe Re? This is based on the expectations.of eachmarket participant...

But recall our analysis of the bonds and money markets; interest ratesexhibit a tendency to converge towards equilibrium: RE .

Thus, we can use:Re = RE ⇒ RE = Rof

Does the EMH make sense?

Consider arbitrage: unexploited profit opportunities. Suppose that forsome asset RE < Rof , so that you (and probably everyone else)predict that in the future that investment on such asset will yield ahigher return than the current equilibrium return.

Then you (and probably many more) will buy such asset driving up itsprice so, the expected return on this asset falls until again RE = Rof .

Note: if RE 6= Rof somebody must be ill-informed

C.E. Tamayo () Econ - 301 July 25, 2011 18 / 20

Rational expectations and the effi cient market hypothesis

But can we observe Re? This is based on the expectations.of eachmarket participant...

But recall our analysis of the bonds and money markets; interest ratesexhibit a tendency to converge towards equilibrium: RE .

Thus, we can use:Re = RE ⇒ RE = Rof

Does the EMH make sense?

Consider arbitrage: unexploited profit opportunities. Suppose that forsome asset RE < Rof , so that you (and probably everyone else)predict that in the future that investment on such asset will yield ahigher return than the current equilibrium return.

Then you (and probably many more) will buy such asset driving up itsprice so, the expected return on this asset falls until again RE = Rof .

Note: if RE 6= Rof somebody must be ill-informed

C.E. Tamayo () Econ - 301 July 25, 2011 18 / 20

Rational expectations and the effi cient market hypothesis

But can we observe Re? This is based on the expectations.of eachmarket participant...

But recall our analysis of the bonds and money markets; interest ratesexhibit a tendency to converge towards equilibrium: RE .

Thus, we can use:Re = RE ⇒ RE = Rof

Does the EMH make sense?

Consider arbitrage: unexploited profit opportunities. Suppose that forsome asset RE < Rof , so that you (and probably everyone else)predict that in the future that investment on such asset will yield ahigher return than the current equilibrium return.

Then you (and probably many more) will buy such asset driving up itsprice so, the expected return on this asset falls until again RE = Rof .

Note: if RE 6= Rof somebody must be ill-informed

C.E. Tamayo () Econ - 301 July 25, 2011 18 / 20

The EMH and market fundamentals

An important implication of the effi cient market hypothesis is thatprices will respond to anouncements only in as much as theinformation being announced is new and unexpected..

Strong version of EMH: prices are not only "correct" but they alsoreflect "market fundamentals"

Market fundamentals: items that have a direct impact on futureincome streams of the underlying security.

Did the Nasdaq free fall from 5,000 points in 2000 to 1,500 points in2001 reflect a dramatic change in market fundamentals?

C.E. Tamayo () Econ - 301 July 25, 2011 19 / 20

The EMH and market fundamentals

An important implication of the effi cient market hypothesis is thatprices will respond to anouncements only in as much as theinformation being announced is new and unexpected..

Strong version of EMH: prices are not only "correct" but they alsoreflect "market fundamentals"

Market fundamentals: items that have a direct impact on futureincome streams of the underlying security.

Did the Nasdaq free fall from 5,000 points in 2000 to 1,500 points in2001 reflect a dramatic change in market fundamentals?

C.E. Tamayo () Econ - 301 July 25, 2011 19 / 20

The EMH and market fundamentals

An important implication of the effi cient market hypothesis is thatprices will respond to anouncements only in as much as theinformation being announced is new and unexpected..

Strong version of EMH: prices are not only "correct" but they alsoreflect "market fundamentals"

Market fundamentals: items that have a direct impact on futureincome streams of the underlying security.

Did the Nasdaq free fall from 5,000 points in 2000 to 1,500 points in2001 reflect a dramatic change in market fundamentals?

C.E. Tamayo () Econ - 301 July 25, 2011 19 / 20

The EMH and market fundamentals

An important implication of the effi cient market hypothesis is thatprices will respond to anouncements only in as much as theinformation being announced is new and unexpected..

Strong version of EMH: prices are not only "correct" but they alsoreflect "market fundamentals"

Market fundamentals: items that have a direct impact on futureincome streams of the underlying security.

Did the Nasdaq free fall from 5,000 points in 2000 to 1,500 points in2001 reflect a dramatic change in market fundamentals?

C.E. Tamayo () Econ - 301 July 25, 2011 19 / 20

Beyond the EMH: bubbles and behavioral finance

It’s hard to explain some episodes of swings in stock prices only bychanges in "fundamentals".

Variables other than fundamentals may influence stock prices:phsycological issues and the institutional structure of the marketplace.

Rational bubbles.

Irrational exhuberance: overconfidence and social contagion.

C.E. Tamayo () Econ - 301 July 25, 2011 20 / 20

Beyond the EMH: bubbles and behavioral finance

It’s hard to explain some episodes of swings in stock prices only bychanges in "fundamentals".

Variables other than fundamentals may influence stock prices:phsycological issues and the institutional structure of the marketplace.

Rational bubbles.

Irrational exhuberance: overconfidence and social contagion.

C.E. Tamayo () Econ - 301 July 25, 2011 20 / 20

Beyond the EMH: bubbles and behavioral finance

It’s hard to explain some episodes of swings in stock prices only bychanges in "fundamentals".

Variables other than fundamentals may influence stock prices:phsycological issues and the institutional structure of the marketplace.

Rational bubbles.

Irrational exhuberance: overconfidence and social contagion.

C.E. Tamayo () Econ - 301 July 25, 2011 20 / 20

Beyond the EMH: bubbles and behavioral finance

It’s hard to explain some episodes of swings in stock prices only bychanges in "fundamentals".

Variables other than fundamentals may influence stock prices:phsycological issues and the institutional structure of the marketplace.

Rational bubbles.

Irrational exhuberance: overconfidence and social contagion.

C.E. Tamayo () Econ - 301 July 25, 2011 20 / 20