Portfolio Allocation and the demand for assets
Click Here for a graphic depicting portfolio allocation in the US and Here for more assets to
choose from (a plug for money and banking?)
We will make the following simplification as the book does – we separate the many assets in
to monetary (money) and non-monetary assets (everything else).
There are three main determinants of asset pricing with each asset having somewhat unique
characteristics.
1) Expected return: The higher the expected return of the asset, all else constant, the higher the
price of the asset. We assume money (C+D) earns a nominal return of zero and a real return
equal to the ‘negative’ of the inflation rate.1 Non-monetary assets have an expected return of inm.
Note, that with QE2, the Fed is purposely lowering the expected return on bonds so that people
buy other non-monetary assets like stocks! We have discussed this many times before!
Asset price = f (Rete) :
+
{stated as “the asset price is a positive (+) function (f) of it’s expected return (Rete), all else
constant}
2) Liquidity: Liquidity is an attractive quality in any asset and a highly liquid asset has three
qualities:
1) it is easy (low cost) to convert the asset into money where money is defined as
transactions money
2) it can be converted to money quickly
3) the amount that it is converted to is representative of its fundamental value (i.e., I can
sell my house very quickly and easily for $5, but that doesn’t mean it is liquid!).
Typically, the more liquid the asset, the lower the return. Take money, typically considered to be
the most liquid asset of all.
Liquidity is especially attractive in a highly uncertain environment. We will ‘say’ more
about his in a moment.
Asset price = f (Liq) :
+
{stated as “the asset price is a positive (+) function (f) of it’s liquidity (Liq), all else constant}
1
Suppose inflation over a year is 10% and I keep $100 in my pocket. That $100 next year would be able to
purchase 10% less in real goods and services given the 10% rise in the general price level that has occurred
over the year.
3) Risk: The more risky the asset, the more uncertain as to the assets’ return. Risk arises for a
variety of reasons and we assume that all else equal, investors prefer assets with less risk (i.e., on
average, investors are risk averse). We also note that risk and expected return are related –
typically, the higher the risk, the higher the expected return (investors require a higher
expected return to take on the higher risk).
Asset price = f (Risk) :
{stated as “the asset price is a negative (-) function (f) of it’s Risk, all else constant}
APPLICATION – examining the behavior of these three main characteristics at the height of the
financial crisis – i.e., the fall of 2008. – click Here and zoom in on what was happening during
the fall of 2008.
So during this time, the demand for money rose dramatically, since money is more liquid
(liquidity is highly desirable in a crisis!), ii is less risky, and the expected nominal return of zero
is a lot better than a negative one (money under the mattress is better than losing it in the stock
market).
MONEY DEMAND –
The other half of the money market - money demand
There are quite a few determinants of money demand
First –inm , the (opportunity) cost of holding money is the interest foregone by holding the nonmonetary asset we typically call a bond (inm). The higher the interest rate, the higher the cost of
holding money so the less money you will hold. This idea gives us a negatively sloped money
demand as shown below.
Second – real income (denoted Y) – if your real income goes up you will conduct more
transactions and in order to conduct more transactions, you need to hold more money.
Graphically, an increase in real income (economic growth) shifts the money demand curve
to the right (i.e., you desire to hold more money at any given interest rate)
Third – Prices – if prices go up, you need more money to conduct the same number (amount) of
transactions. In fact, we assume that nominal money demand is proportional to the price level.
For example, if prices rise by 4% then nominal money demand will rise by 4%. Since we deal
with real money supply and real money demand, we can derive a general form of real money
demand as follows (the text does this on pages 253 and 254)
1) Md = P x L(Y, i) L is a function to be determined – but we know a few things from above - Md is positively
related to P and Y and negative related to i (note i = inm).
Noting that i = r+ πe and using the proportionality assumption, we can re-write 1) as
2) Md/P = L(Y, r+πe)
A more specific money demand function is in order – this one is from a numerical problem from
the back of chapter 7
3) Md/P = 500 +.2Y – 1000(r+πe)
Note that 3) is consistent with real money demand being a positive function of real income (GDP)
and negatively related to the nominal interest rate.
THE INTERCEPT IN THE REAL MONEY DEMAND EQUATION – VERY IMPORTANT!
Beyond the three determinants of money demand, there are others – and given the recent
financial crisis, these other determinant have played a critical role
Fourth determinant of real money demand – the liquidity of non-monetary assets – if the
liquidity of non-monetary assets falls, all else constant, money demand will increase since money
is the most liquid asset on the earth and liquidity is a desirable quality. The result is a rightward
shift in the money demand function – even though real income (Y) and i = r+πe did not change.
Fifth determinant of real money demand – risk on non- monetary assets – if the risk on nonmonetary assets rises, all else constant, then money becomes more attractive since we assume that
people are risk averse, all else constant.
Given the financial crisis, especially during the fall of 2008, we can characterize the situation
with simple graph of the money market.
Now, what should the Fed do?? If they do nothing, then real rates will rise which is exactly what
we DON’T NEED given the financial panic. In addition, the Fed gained authority to pay interest
on reserves (both required and excess) in October, 2008. We know from our money supply
discussions and especially money supply problem #1, that the real money supply will shift to the
left, exacerbating the increase in interest rates due to the two portfolio shocks to money demand.
In summary, the Fed was facing an increase in money demand and a decrease in money supply
during the fall of 2008, both of which will increase the real rate – to offset this, the Fed needs to
conduct massive amounts of open market purchases. Click Here to see if they did (look at the
data during the fall of 2008)!
How does the story change given the new economy during the mid to late 1990s?
Other Determinants of Money Demand –
So far, we have that nominal money demand is a function of positive function of P, Y and risknm
and a negative function of i( = r + πe) and liqnm.
In principles and elsewhere, you probably have the nominal interest rate on the vertical axis, since
the opportunity cost of holding non-interest bearing money is in fact the nominal interest rate.
But since we have been working with real interest rates throughout the semester and desire to
continue to do so, we place r on the vertical axis and hold inflationary expectations (πe) constant
so in effect, inflationary expectations becomes a shift variable.
Example: if we set πe = 0, then i = r. (i.e., r = i – πe). Now if πe rises to 2% and we assume that r
stays the same, then i must rise by 2% as well – that is, the cost of holding money has gone up, at
the same real interest rate. The influence is that the money demand function will shift to the left
(i.e., money demand is negatively related to πe, all else constant). See graphic below.
Final Determinants of Money Demand
Wealth – an increase in wealth will cause people to hold more money, since higher wealth
typically means more transactions. We need to remind ourselves that wealth is a stock variable
where income (y) is a flow variable.
Interest rate on money - If banks all of a sudden start paying interest on m, denoted im, then all
else constant, people will hold more money.
Efficiency of Payment Systems – years ago, this determinant of money demand was very
relevant. Now, we can pretty much ignore this determinant but through the years, the increase in
the efficiency of payment systems has resulted in people holding less money, since it is easy to
transfer money in savings to money in checking, in fact, many banks do this automatically if you
overdraw.
Identifying the shocks to real money demand is a very big deal when it comes to monetary policy,
If money demand increases because of a nominal shock such as the risk of non-monetary assets
rising, then the Fed should not only accommodate the shock, they should conduct enough open
market purchases so that the real rate falls and thus, we might be able to offset the negative shock.
Conversely, if the shock to money demand is real, that is, money demand is increasing due to
higher output, then the Fed should worry about overheating and thus ‘allow’ real rates to rise to
prevent inflation from accelerating. All told, it is critical for the Fed to identify the shocks since
the appropriate policy response depends critically on the source of the shock.
The quantity theory of money and the equation of exchange
Another way to view supply and demand for money is through the equation of exchange:
MV = PY
Where M is the nominal money balances, V is the velocity of money (the number of times a
dollar bill turns over in a years time), P is the general price level, and Y is real output (GDP).
Example – island economy with one good, bicycles. In 2010, there were 50 bicycles produced at
a price of $100 per bicycle. So nominal GDP (P times Y) is $5000. We also have a nominal
money supply equal to $1000. What is V? V = 5, which means, each dollar exchanges hands
(turns over) 5 times per year.
MV = PY = $1000 x 5 = $100 x 50
If we take the percent change of the equation of exchange, also known as the quantity theory of
money, we have:
%∆M + %∆V = %∆P + %∆Y
The equation above is extremely useful. Consider the following: Let us assume that V is
constant so that the %∆V = 0. If we go to the right hand side, what is the %∆ in P called? What
is the %∆ in Y called? Do we have any notion as to the optimal values of these two important
macroeconomic variables? Hint, the cruise ship example.
So let us write out the equation with the above information:
%∆M + 0 = 2% + 3%
Which implies that the Fed should allow the nominal money supply to grow at 5%. In fact, this
equation is often associated with Milton Friedman, who was a classical economist and among
many other famous quotes once said that:
“Inflation is always and everywhere a monetary phenomenon”
Let us apply this statement to the equation of exchange
Suppose the Fed bumps up money growth from 5% to 8%. Assuming that 1) Velocity is constant
and 2) we are in a classical world so that Y is determined by the production function meaning that
changes in M do not effect output (i.e., the aggregate supply curve is vertical), then the increase
in the growth rate of the money supply will result in an equal change in the rate of inflation.
Using the equation of exchange:
We started with:
5% + 0% = 2% + 3%
Then we have:
8% + 0% = 5% + 3%
And therefore “Inflation is always and everywhere a monetary phenomenon”
since the increase in inflation was caused by excessive money growth. In fact, Milton wanted to
kick the monetary policy steering wheel off of the cruise ship and replace it with a robot
that allows the money supply to grow at constant rate, depending on what is going on with
the velocity of money.
More on the velocity of money. To help us understand what makes the velocity of money ‘tick,’
we can apply the episode of the fall 2008 when we were at the peak of the financial crisis. As we
know, money became an extremely attractive asset during this time given the fear on nonmonetary assets (except for US Treasuries – often referred to as the safest asset on the earth).
The increase in money holdings during this time, holding P and Y constant, means that the
velocity of money has fallen! This makes sense since in effect, households are hoarding money so
that each dollar is now turning over less. What are the implications for monetary policy? Let’s
start with our original set up and then let the velocity of money fall by 10%, all else constant.
.
5% + 0% = 2% + 3%
then
5% + (-10%) ≠ 2% + 3%
but we know this cannot be! Something must change so that the equation is satisfied! Since
classical economists believe that prices are perfectly flexible, then we have the following:
5% + (-10%) = (- 8%) + 3% AHHHH! This is deflation
So what must the Fed do to avoid this CENTRAL BANKING
NIGHTMARE????? You got it, pump up the money supply to ?????
15%
15% + (-10%) = 2% + 3%
In other words, when velocity falls the Fed better react and offset the
fall in velocity by pumping up the money supply to prevent deflation.