Tutorial assignment: week 4 2022
Answer guide
1. Using information from the RBA web site, identify two periods in this century when the rate of growth of the Currency aggregate in Australia exceeded 10 per cent. What were the significant events in these periods that might explain higher than normal growth in Currency?
There are two places in the RBA site where this information can be readily found.
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· In graphical form, this information is presented in the RBA chart pack [navigating from home page: Chart Pack>>Credit and Money>>Monetary Aggregates Growth] to find the following graph (which was also presented in the lecture):
· In numerical form, figures for the level of currency (but not the growth rate) can be found in the Statistics section of the site in Table D3, column B [Statistics>>Economic and Financial Statistics>>Monetary Aggregates – D3]. You would need to calculate percentage changes in these figures to answer the question.
Using the graph above, we can easily read off an answer to the first part of the question. Currency growth exceeded a 10 per cent annual rate in 2008-9 and again in 2020-21. Significant events that could explain these high rates of currency growth:
· 2008-9: the GFC. During this period there was a lot of uncertainty about economic prospects as the world economy went into recession, banks failed and the value of many investments such as equities was falling. In these sorts of conditions, households tend to prefer the safety of cash and will try to hold a larger proportion of their wealth in that form. At the same time, governments in Australia and abroad were making cash more readily available to households and businesses through stimulus payments to counteract the effects of the GFC. In Australia for example there were cash payments of $950 made to taxpayers in February 2009. These would have been paid into bank accounts, but to the extent that they were withdrawn and spent as cash, they would have added to currency growth. Similar policy actions were being taken in other economies.
· 2020-21: this was another time of major uncertainty due to the pandemic. Again, because of the uncertainties householders preferred to hold a larger proportion of their financial wealth in cash, and the government again was making significant payments to households and businesses to support the economy and alleviate financial stress.
2. During the first of the periods identified above, what was happening to the growth of M3? What factors might explain an increase in Currency growth and a slowing in M3 growth occurring at the same time?
The growth of M3 was decelerating sharply during that period (see graph).
While the growth rates of the different monetary aggregates can often differ by significant amounts, it is unusual for their growth rates to move sharply in opposite directions. When this happens, it is likely to signify some event that is having a major impact on the relative attractiveness of bank deposits compared to currency. (This didn’t happen, for example, in the 2020-21 episode.)
In the 2007-9 period, while currency growth was increasing, the annual growth rate of M3 slowed down from nearly 25 per cent to less than 15 per cent by 2008, and continued to slow down over the following year. The fact that these two growth rates were moving in opposite directions for a period of time can be explained by the nature of the financial crisis that was occurring. The M3 aggregate is equal to Currency plus bank deposits. During this period, people were losing confidence in the safety of banks. Some were withdrawing funds from bank deposits in order to build up their cash holdings. Others may have chosen to increase their bank deposits more slowly than previously in order to increase cash holdings more quickly. So the two growth rates were moving in opposite directions. As confidence in the banks was restored over the following two years, the rates of growth of the two aggregates again converged.
3. The phenomenon of ‘dollarisation’ in an economy is said to occur when a significant proportion of residents prefer to make their transactions in US dollars rather than in the official domestic currency. Why might this occur, and why would this phenomenon be more common in some countries than in others?
One of the functions of money is store of value. This requires money to have a stable and predictable purchasing power. In other words, it requires an economy with low and stable inflation of prices expressed in that currency. Dollarisation typically occurs in economies that have either high inflation, or a high fear of inflation.
If money is unable to perform the store of value function efficiently, this will also undermine the other functions of money, especially the medium of exchange function. One of the desirable characteristics of a medium of exchange is that money must be widely accepted. But if it is not expected to maintain a stable value, no one will want to hold it and so it won’t be widely accepted as a means of payment. These things reinforce each other.
This explains why dollarisation is more common in some economies than others. Dollarisation is particularly likely to occur in countries with a history of high inflation. Historically, Latin American countries and some African countries have experienced significant dollarisation.
4. Consider a simple economy consisting of the following three persons:
Ito is a hairdresser who needs to get some building work done
Rav is a builder who needs someone to do car repairs
Esta is a motor mechanic who needs a haircut
Describe the difficulties that would be encountered in arranging mutually beneficial exchange among these three if there were no such thing as money.
There are three types of product in this example, with one producer and one consumer for each product. In principle, therefore, there can be a mutually beneficial outcome where each producer engages in their specialist productive activity and each is able to obtain their desired product from a service provider. But this can only be achieved if there is some coordination mechanism amongst the three individuals, since there is no double coincidence of wants anywhere in this economy. If, for example, Rav had wanted a haircut rather than car repairs, then Rav and Ito could make a direct exchange: a haircut in exchange for some building work. But in the absence of such a double coincidence of wants, any exchange that occurs would have to be based on some system of promises and trust.
An example of how that could work would be the following.
Example: Ito employs Rav to do the building work and pays Rav with a haircut voucher (a promise to give the holder a haircut). Rav hires Esta to do the car repairs and pays with the haircut voucher already received from Ito. Then Esta takes the voucher to Ito and receives a haircut.
Observations:
· In the above example, three-way mutually beneficial exchange has occurred
· but, this is a cumbersome way to do it
· it only works if Rav’s original promise can be relied upon
· to the extent that this is the case, Rav’s haircut voucher functions as a de facto form of money in this system, since it is be used by all three as a medium of exchange
5. Consider a different example of three-way trade involving goods rather than services:
Alfa produces firewood for fuel
Betta produces a wheat crop for food
Gammo produces wool for clothing
Each person has a demand for some mix of all three products: food, fuel and clothing. Why would barter exchange be more likely to succeed in this situation than in the previous question? Why would it still be beneficial to introduce money into this economy?
Non-monetary (or barter) exchange would be easier in this economy than in the previous example for two reasons:
· First, the products being traded are goods rather than services, and the goods are storable. This means there is no need for exchanges to be based on promises. Alfa might engage in a trade with Betta which results in Betta having more firewood than desired, but Betta can store the surplus and use that in a further exchange with Gammo. No promises or trust are required.
· Second, in this example each producer has a demand for some quantity of all three products. So there will be some instances of double coincidence of wants. For example, Alfa produces firewood and requires some wool from Gammo, while Gammo desires some amount of the opposite exchange. So there will be situations where two-way barter exchange is mutually beneficial. This was not the case in the previous example.
Further comments
In this example, non-monetary exchange is possible but it would still be cumbersome and inefficient. For example, storing surplus firewood for subsequent resale would be a costly way to engage in three-way trade compared with using a mutually accepted form of money as a medium of exchange.
There is also the time dimension to consider. One producer may have an overall surplus of income in a given time period while another has a deficit. In an efficient system there needs to be store of value so that the person with the surplus can save in order to spend later. Storing the physical commodities is a possible way of doing this, but it is inefficient because these commodities are not permanently durable (one of the requirements of money) and are costly to store and to transport (the portability requirement of money)
6. (1 mark each, answers to two decimal places where applicable)
(a) What is the yield to maturity on a discount bond that has a face value of $8000, is three years from maturity and is currently trading at $7450?
The yield to maturity is the interest rate that equates price (P) to present value (PV)
(b) What is the present value of a three-year coupon bond which has a face value of $1000, a coupon rate of 1.5 per cent and a yield to maturity of 2 per cent?
The security pays a coupon of $15 each year and a final principal repayment of $1000. The interest rate for calculating present values is i = .02
So the three-year stream of payments is (15, 15, 1015).
We calculate the present value of this stream using the interest rate to discount future cash flows as follows:
7. (1 mark each, answers to two decimal places where applicable)
(a) What is the market price of a discount security which matures in 2 years’ time, has a face value of $5000 and a yield to maturity of 1.8 per cent?
The market price is equal to the present value (PV) of the security. The future cash flow (CF) is $5000. The discount factor of (1 + i) is equal to 1.018
So, the price of the security is
which gives the result, PV = $4824.75
(b) What is the market price of a discount security which matures in 3 years’ time, has a face value of $8000 and a yield to maturity of minus 2.5 per cent?
Again, the market price is equal to the present value (PV) of the security.
CF = $8000.
Here the discount factor (1 + i) is equal to (1 – 0.025) = .975
So the price of the security is given by,
which gives the result, PV = $8631.30
Notice that when the yield to maturity is negative, the market price is higher than the face value. Another way of putting it is that if you buy the security now, you are repaid less than you invested when the security matures.
8. (1 mark each, answers to two decimal places where applicable)
(a) Calculate the market price of a consol with a coupon of $200 per annum and a yield of 2.6 per cent.
The formula that relates price, yield and coupon for a consol is:
Here C = $200 and
Which gives: P = $7692.31
(b) Suppose you had purchased this consol at the price calculated above. After your purchase, suppose the yield on these securities falls to 1.7 per cent. Calculate the new price of the consol and the gain or loss you have incurred.
The new price is given by
So P’ = $11,764.71
You have made a gain of P’ – P = $4072.40
Note that yield and price always move in opposite directions, so when the yield falls, the holder makes a gain.
9. In general, if you have purchased a long-term government bond and the yield to maturity falls by 0.5 per cent after you purchased it, would you be better or worse off? In that situation, would you prefer this to be a 10-year bond or a 5-year bond? Explain the reasoning for your answer.
For the reason explained in the previous question, price and yield move in opposite directions. So you are better off in this situation. Furthermore, when the yield moves by any given amount, the effect on price will be larger the longer the term to maturity. So in this case, you would prefer to be holding the 10-year bond because the capital gain would be larger.
10. Suppose you are a first homebuyer considering taking out a mortgage. You are offered a 30-year mortgage at an interest rate of 4.5 per cent fixed for the life of the loan. How would your assessment regarding the desirability of taking the loan be influenced by your current income, your expectations about future inflation and your expectations about future movements in housing prices?
Current income: The higher your income the greater will be your capacity to meet the interest and repayment requirements on the loan. A borrower would normally try to make an estimate of the amount of income they have available to service the loan by taking total income and deducting regular expenses, and allowing a buffer for unpredictable contingencies like illness or temporary loss of employment. If you are self employed (eg a small business owner) you might need to allow a buffer for unpredictable variation in income.
Inflation expectations: In a high inflation environment it will get easier to service a fixed loan over time as prices and incomes rise. Although regular expenses will also be rising along with the general price level, the proportion of your income spend in servicing the loan will decline over time because the loan payments are fixed. So if you expect a high average inflation rate in the years ahead you would be more likely to consider the loan to be affordable.
Expected housing prices: If you expect housing prices to rise at a fast rate in the future you might consider it more attractive than it would otherwise be to take out the loan. Hence you might be willing to stretch your budget a bit further to do this than you would otherwise. This is for two reasons: first, if you think you will eventually need to buy a house anyway at some stage, it’s better to buy now rather than later when you expect the price to be higher; and second, you might take the view that, even if you get into financial difficulty in servicing the loan, you can sell the house, repay the loan and make a capital gain. All of this assumes that your expectations turn out to be correct, which is a risk factor in any of these sorts of decisions.
201620112006200119962021 0 5 10 15 20 % 0 5 10 15 20 % MonetaryAggregatesGrowth Year-ended M3 Currency Sources:APRA;RBA
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