Expectations Flashcards
expected present discounted value
the value today of a sequence of future payments
discount factor
1/1+it
If payments today or expected future payments increase what is the effect on the present value?
It increases
What is the effect if the current and future interest rates increase?
Decrease in the present value
present value for a constant sequence of payments
€Vt=€z/i
Two ways of writing the present value
By finding the present value in nominal terms and dividing by the price level or compute the present value in real terms
Default risk
the risk that the issuer of the bond will not pay back the full price promised by the bond
Maturity
the length of time over which the bond promises to make payments
Yield to maturity
the interest rate associated with the bond. that constant rate annual interest rate that makes the bond price today equal to the present value of future payments on the bond
Yield curve
the relation between the % yield of the bond and the maturity of the bond. Can also be deemed a term structure
Price of a one year bond
€P1t=FV/1+i1t
The price of the one-year bond varies inversely with the one year nominal interest rate
Price of a two year bond
€P2t=FV/(1+i1t)(1+iet+1)
Price of the two year bond depends inversely on both the current one year rate and one year expected rate
expectations hypothesis
investors care only about the expected return
arbitrage
the fact that two relations must be equal. should be no profit from doing nothing
the approximation relation between a two year interest rate and then current one year interest rate and the the expected one year interest rate?
(1+i2t)^2=(1+i1t)(1+iet+1)
by using this we get the approximation
i2t≈1/2 (i1t+ie1t+1)
i.e the average of the two
When the yield curve is upward sloping it tells us….
long term interest rates are higher than short term interest rate
When the yield curve is downward sloping it tells us that…
short term interest rates are higher than long term
ex-dividend price of a stock
Det+1 + Qet+1 /Qt
Price of a stock today
Due to arbitrage must be equal to the present value of the expected dividend plus the present value of the expected stock price next year
Higher expected future dividends leads to…
higher real stock price
Higher current and expected future one-year real interest rates lead to…
a lower real stock price
What effect does expansionary policy have if the central banks move was only partly expected?
as expansionary monetary policy implies lower interest rates for a time and also a higher output. With a lower output and greater dividend stock prices will increase.
What happens to the stock price when there is a shift in the LM curve?
Leads to higher output which would increase stock prices but also higher interest rate which would lead to lower stock prices. Depending on the slope of the LM curve determines which effect dominates. Steeper LM curve means small increase in output but large increase in the interest rate therefore stock prices are more likely to decrease
How the central could react to the shift in the IS curve (increased consumption)
- Accommodate the shift in the IS by increasing the money supply to avoid an increase in the interest rate and increase output higher also increasing stock prices
- Leave the LM curve unchanged and just move along it and what happens to stock prices will be ambiguous
- Worry that an increase in output will cause too high of inflation to shift the LM curve upwards to big output back down but increasing interest rates in the process. and stock prices will surely go down
How stock prices respond to a change in output depend on three things…
- What the market expected in the first place
- the source of the shocks behind the change in output
3 how the market expects the central bank to react to the change in output
equity premium
the risk premium investors require in order to hold stocks rather than bonds due the fact that people are generally risk averse.
The higher the equity premium…
the lower the stock price do to it being incorporated in the discount factor.
rational speculative bubbles
stocks prices may increase purely because investors expect them to
Permanent income theory
emphasises that consumers look beyond current income
Life cycle theory
consumers’ natural planning horizon is their entire lifetime
How would a foresighted consumer decide how much to spend
- Add up the value of the stocks and bonds he owns, the value of his current accounts, the value of a house minus the mortgage still due etc. This would give him an idea of his financial and housing wealth. also known as non-human wealth He would also estimate his total lifetime after tax labour income. This is know as human wealth.
- Add human and non-human wealth to get total wealth
What is the assumption made about total wealth?
The consumer will decide to spend a proportion of his total such as to maintain roughly the same level of consumption each year throughout his life
If his the level of consumption was higher than his current income he would…
borrow
If his level of consumption was lower than his current income he would…
save
Intertemporal budget constraint
represents all the combinations of current and future consumption that the consumer can choose given the present value of their endowment.
consumption smoothing
the preference for a balanced consumption path over time
Fault with the foresighted approach
may not want constant consumption over lifetime. Defer spending for more expensive activities until later
The calculations exceed expectations
Forecasts based on what is expected to happen and doesnt factor in unexpected events such as not being able to work
bank might not be willing to lend you money
Consumption function of a foresighted person
Ct=C(total wealth, YLt - Tt)
Where
Wt=WFt +WHt +Σ[(Yet+i - Tet+i)/(1+r)^i]
Consumption is an increasing function of total wealth and of current after tax labour income. Total wealth is the sum of human and nonhuman wealth
Why does consumption react a lot to changes in current income?
Consumption is very sensitive to changes, more so than expected from the theories, to temporary changes. It could be due to consumers not being able to obtain credit easily - subject to liquidity constraints
What happens if expected future output increase?
Expected future labour income increases Human wealth increases consumption increases expected future dividends increase stock prices increase non-human wealth increases consumption increases
Two main implications of dependence of consumption on expectations for the relation between consumption and income
Consumption is likely to react less than one-for-one to fluctuations in current income. If the decrease in income is permanent then they may decrease if one-for-one but if it is seen as temporary then the will decrease just not by as much.
Optimism about the future can also cause an increase in the consumption without actual changes in income
What must be take into account when making investment decisions?
The depreciation rate of the ‘machine’ . So when you buy it will be worth K but a year later it will be K(1-δ) and K(1-δ)^2 a year after that
When computing the expected profits what must be taken into account
the depreciation rate and then the real interest rates. we discount by the real interest rates and multiply by the depreciation factor
How is the decision whether to buy a machine or not made?
If the present value of the profits exceeds the present real value of the costs then the firm should invest
Investment in an economy depends…
positively on the expected present value of future profits. The higher the current or expected future profits the higher the level of investment. The higher current or expected future real interest rates the lower the expected present value and thus the lower the level of investment
static expectations
where both expected future profits and future real interest rates remain at the same level as today. and thus the investment function becomes
V(Πet)=Πt/rt+δ
rental cost of capital
the sum of the real interest rate and the depreciation rate
interpretation of the investment function I=I(Π/r+δ)
investment depends on the ratio of profit to user cost. The higher the profit, the higher the level of investment
A better interpretation of investment behaviour
investment depends both on the expected present value of future profits and on current level of profits
It=I[V(Πet), Πt]
Profit per unit capital is….
an increasing function of the ratio of sales to the capital stock.
What can affect a firms investment decisions?
In the same way as consumption, it is dependent on whether the change is perceived to be temporary or permanent. The more temporary it seems the less likely they are to revise investment strategy and not invest in new machines or buildings i.e the boom before xmas
Consumption and investment typically
move together
Investment is
more volatile that consumption
Because investment contributes a smaller proportion to GDP…
movements in consumption and investment are roughly of the same magnitude
aggregate private spending
the sum of consumption and investment spending
A(Y,T,r) ≡ C(Y-T)+I(Y,r)
What does the IS relation become when we substitute consumption and investment for aggregate private spending?
Y=A(Y,T,r)+G
APS is an increasing function of Y. Increase in Y means an increase in consumption and investment.
APS is a decreasing function of taxes: higher taxes decreases consumption
APS is a decreasing function of the real interest rate: higher r means decreased investment
What does the IS relation look like when we extend the model to incorporate expectations?
Y=A(Y,T,r,Y’e,T’e,r’e)+G
What does the IS curve look like now when we include the extended aggregate private spending?
A steeper line as apart from Y and r everything else is take as a given.
Why is the multiplier likely to be small?
The size of the multiplier depends on the size of the effect of a change in current income (output) has on spending. But a change in current income given unchanged future expectations of future income, is unlikely to have a large effect on spending
A change in any other variable other than a change in r or Y will result in…
a shift in the IS curve
In terms of the decision to hold money(in regards to the LM relation) the decision is…
myopic. It doesnt depend on future expectations. It depends primarily on current income and the current short term interest rate.
What is the interest rate that the central bank alters
current nominal interest rate
What interest rate does spending in the IS relation depend on?
Both on current and expected future real interest rates
Implementation of monetary policy on the two-period IS-LM model (example of monetary expansion)
To begin with the LM curve will shift downwards resulting in an increase in output and a decline in the interest rate. With this decreased interest rate and higher output financial markets now anticipate lower interest rates in the future also. In doing so this shifts the IS relation to the right.
Quantitative easing
operations in which, while at the zero lower bound, the central banks continues to open market operations to increase the money supply, either by buying T-bills or long maturity government bonds.
Effect of quantitative easing on future expectations
one of the qualifying arguments for quantitative easing. If the increase in the money supply is take as a signal by markets that the central bank will continue to follow a very expansionary policy this will increase spending today
In the liquidity trap inflation…
is good. If people expect inflation to be higher in the future it will increase spending today.
Effect of decreasing the budget deficit (through cutting G)
G goes down shifting the IS curve to the left. At a given interest rate, spending is decreased and output is decreased. Expected future output goes up and shifting the IS curve to the right. At a given IR output and private spending increase. The expected future rate goes down leading to a further shift to the right.
Effect of a reform on the social insurance system - reduction in the generosity of benefits
Adverse effect: reduction in the consumption of the unemployed
Positive effect on spending through expectations: the anticipation of higher output in the future will lead to higher consumption and investment
Factors which affect whether a budget deficit reduction will increase output in the short run..
The credibility of the program: spending cuts or increased taxes in the future?
Timing of the program: how large a future spending cuts relative to current spending cuts
The composition of the programme: does it remove distortions in the economy?
The state of the government finances in the first place
