Question 119 market efficiency, fundamental analysis, joint hypothesis problem
Your friend claims that by reading 'The Economist' magazine's economic news articles, she can identify shares that will have positive abnormal expected returns over the next 2 years. Assuming that her claim is true, which statement(s) are correct?
(i) Weak form market efficiency is broken.
(ii) Semi-strong form market efficiency is broken.
(iii) Strong form market efficiency is broken.
(iv) The asset pricing model used to measure the abnormal returns (such as the CAPM) is either wrong (mis-specification error) or is measured using the wrong inputs (data errors) so the returns may not be abnormal but rather fair for the level of risk.
Select the most correct response:
When reading The Economist magazine, your friend is reading publicly available information. If the views and opinions of the magazine are helpful for selecting stocks with positive expected abnormal returns, then as soon as the magazine is published and made public, stock prices should adjust to reflect the new information revealed in the magazine. This would occur if markets are informationally efficient, which is semi-strong form efficiency. Therefore there would be no future positive expected abnormal returns from reading the magazine since stock prices would instantly incorporate the information, so the under-priced share prices would rise and the over-priced share prices would fall, meaning that there are no more 'free lunches' to be had, all assets would be fairly priced.
But if your friend can use the magazine's information to make positive expected abnormal returns, then markets must be semi-strong form inefficient, so semi-strong form efficiency is broken. Alternatively, the model used to measure the abnormal returns could be broken. Or both the model is broken and semi-strong form efficiency is broken. Note that if semi-strong form efficiency is broken then strong form efficiency must also be broken.
Technical traders:
'Technical traders' look at past stock price charts and trends, and they beleive that the theory of weak form market efficiency is broken. They think that past prices and returns are useful for predicting future prices. They are optimists who think they can beat the market (without taking on more risk), and do not beleive that prices are a random walk.
Contrast this with 'fundamental traders' who believe that publically available news can be used to predict future stock prices. They read annual reports as well as industry, economic and demographic analysis and make decisions based on this publically available data. Unlike technical traders, fundamentalists doubt that past price patterns are useful for predicting the future. Fundamentalists think that markets are weak form efficient, but semi-strong form inefficient. Warren Buffett and Charlie Munger of Berhshire Hathaway are two famous fundamentalist investors. They would also call themself 'value' investors rather than growth or glamour investors.
Fundamentalists who analyse company financial reports and news announcements (but who don't have inside information) will make positive abnormal returns if:
If fundamentalists make returns above the return that they deserve, for the level of systematic risk that they take on, then they earn positive abnormal returns and semi-strong form market efficiency must be broken. Therefore markets must be semi-strong form inefficient.
Fundamentalists benefit from semi-strong form market inefficiency. Chartists, another name for 'technical traders', benefit from weak form market inefficiency.
According to Eugene Fama, who constructed this theory, the levels of market efficiency are built on one another, so if markets are weak form inefficient then they are also semi-strong and strong-form inefficient which means that all forms of efficiency are broken.
The theory of fixed interest bond pricing is an application of the theory of Net Present Value (NPV). Also, a 'fairly priced' asset is not over- or under-priced. Buying or selling a fairly priced asset has an NPV of zero.
Considering this, which of the following statements is NOT correct?
From the bond pricing formula, the required return r is in the denominator of each fraction so any increase in r causes a decrease in the price P and vice versa:
###P_\text{0, bond} = C_\text{1,2,3,...,T} \times \frac{1}{r}\left(1 - \frac{1}{(1+r)^{T}} \right) + \frac{F_\text{T}}{(1+r)^{T}} ###When the required return rises, the bond price falls.
When the required return falls, the bond price rises.
This is not only true for bonds but for any asset including shares and land.
The required return of a fairly priced bond is also its IRR. Remember that the IRR is the discount rate that makes the NPV zero.
###\begin{aligned} NPV &= C_0 + \frac{C_1}{(1+r)^1} + \frac{C_2}{(1+r)^2} + ... + \frac{C_T}{(1+r)^T} \\ 0 &= C_0 + \frac{C_1}{(1+r_{irr})^1} + \frac{C_2}{(1+r_{irr})^2} + ... + \frac{C_T}{(1+r_{irr})^T} \\ \end{aligned} ###Re-arranging the bond-pricing equation:
###P_\text{0, bond} = C_\text{1,2,3,...,T} \times \frac{1}{r}\left(1 - \frac{1}{(1+r)^{T}} \right) + \frac{F_\text{T}}{(1+r)^{T}} ### ###\underbrace{0}_{\text{NPV}} = -\underbrace{P_\text{0, bond}}_{PV(\text{cost})} + \underbrace{C_\text{1,2,3,...,T} \times \frac{1}{r_\text{IRR}}\left(1 - \frac{1}{(1+r_\text{IRR})^{T}} \right) + \frac{F_\text{T}}{(1+r_\text{IRR})^{T}}}_{PV(\text{gains})} ###Because the NPV of buying a fairly priced bond is zero, the bond's yield is equivalent to the IRR of buying it too.
Question 339 bond pricing, inflation, market efficiency, income and capital returns
Economic statistics released this morning were a surprise: they show a strong chance of consumer price inflation (CPI) reaching 5% pa over the next 2 years.
This is much higher than the previous forecast of 3% pa.
A vanilla fixed-coupon 2-year risk-free government bond was issued at par this morning, just before the economic news was released.
What is the expected change in bond price after the economic news this morning, and in the next 2 years? Assume that:
- Inflation remains at 5% over the next 2 years.
- Investors demand a constant real bond yield.
- The bond price falls by the (after-tax) value of the coupon the night before the ex-coupon date, as in real life.
Higher inflation reflects higher prices of goods and services, but since bonds are not consumption assets, bond prices will not increase with inflation.
However, higher inflation will reduce the real bond yield. Because we assume that investors demand a constant real bond yield, then the nominal bond yield must increase by approximately the same amount as inflation, which is 2% pa since inflation grew from 3 to 5% pa.
The Fisher equation shows the relationship between nominal and real returns. There is an exact and an approximate formula:
###1+r_\text{real} = \dfrac{1+r_\text{nominal}}{1+r_\text{inflation}}### ###r_\text{real} \approx r_\text{nominal} - r_\text{inflation}###For the nominal bond yield to increase, the bond price must fall. This would have happened today as soon as the news of higher inflation was released. The bond price is likely to have fallen by about 4% because if the coupon rate is low then the bond price is mostly affected by the change in the present value of the face value which is received in 2 years. ###\text{change in present value of face} = 1-\dfrac{1}{(1+0.02)^2} = 0.03883 \approx 4\%###
The bond was originally issued at par which means that the price originally equaled the par (also called face) value. Then the price dropped due to the higher inflation news. But over the next 2 years until the bond matures, the bond price will slowly appreciate back up to its face value. Note that the bond price will fall by the (after-tax) value of the coupon the night before each ex-coupon date, but on each ex-coupon date, the price will be a little higher than the last time, until it reaches the face value. On the day before the final ex-coupon date, the bond price will equal the face value plus the value of the coupon, and then it will fall to zero. This can be best seen in the familiar saw-tooth graph of bond prices.
The efficient markets hypothesis (EMH) and no-arbitrage pricing theory are most closely related to which of the following concepts?
Competition and the idea that firms operating in perfectly competitive markets make zero economic profit is most closely related to the idea of the efficient markets hypothesis (EMH) and no-arbitrage pricing theory.
Question 338 market efficiency, CAPM, opportunity cost, technical analysis
A man inherits $500,000 worth of shares.
He believes that by learning the secrets of trading, keeping up with the financial news and doing complex trend analysis with charts that he can quit his job and become a self-employed day trader in the equities markets.
What is the expected gain from doing this over the first year? Measure the net gain in wealth received at the end of this first year due to the decision to become a day trader. Assume the following:
- He earns $60,000 pa in his current job, paid in a lump sum at the end of each year.
- He enjoys examining share price graphs and day trading just as much as he enjoys his current job.
- Stock markets are weak form and semi-strong form efficient.
- He has no inside information.
- He makes 1 trade every day and there are 250 trading days in the year. Trading costs are $20 per trade. His broker invoices him for the trading costs at the end of the year.
- The shares that he currently owns and the shares that he intends to trade have the same level of systematic risk as the market portfolio.
- The market portfolio's expected return is 10% pa.
Measure the net gain over the first year as an expected wealth increase at the end of the year.
Since the share market is weak-form efficient, there's no use trying to predict price movements from past prices and returns (technical analysis) because prices don't follow any pattern, they'll be a random walk whose up and down moves are determined by the release of good and bad news. Of course in the very long run, prices should trend upwards to reflect the time value of money and risk premium, but they bump up and down as price-sensitive news is released.
Since the share market is also semi-strong form efficient, there's no use reading the financial news, because any price-sensitive information will be instantly reflected in share prices.
Since the man has no inside information, his time spent day-trading is wasted since he can only expect to earn the market rate of return which he would earn anyway as a passive buy-and-hold investor. Actually, by actively day-trading he will only rack up transaction costs and lose the potential wages he could have earned doing his old job (an opportunity cost).
Therefore the net gain as a cash flow measured at the end of the year will be the future value of his transaction costs and opportunity costs of not working. Since they are both paid at the end of the year, these amounts can be simply summed:
###\begin{aligned} V_1 &= - (\text{opportunity cost of not working}) - (\text{transaction costs}) \\ &= - 60,000 - 250 \times 20 \\ &= - 60,000 - 5,000 \\ &= - 65,000 \\ \end{aligned}###So the man should not quit his ordinary job and become a day trader. If he does that he'll lose $65,000 at the end of each year.
Note that the expected cash flow he'll earn from having his money invested in shares is not a gain since he would have earned that regardless of his decision to quit his job and become a day-trader or not. Also, the return he earns on the shares is exactly the return he deserves for the risk, so the NPV of investing is zero so there is no gain after adjusting for risk anyway.
A company advertises an investment costing $1,000 which they say is underpriced. They say that it has an expected total return of 15% pa, but a required return of only 10% pa. Assume that there are no dividend payments so the entire 15% total return is all capital return.
Assuming that the company's statements are correct, what is the NPV of buying the investment if the 15% return lasts for the next 100 years (t=0 to 100), then reverts to 10% pa after that time? Also, what is the NPV of the investment if the 15% return lasts forever?
In both cases, assume that the required return of 10% remains constant. All returns are given as effective annual rates.
The answer choices below are given in the same order (15% for 100 years, and 15% forever):
One hundred year case
Since there are no dividends, the expected total return is all capital return ##(r_\text{expected capital}=0.15)## and the value of the investment in 100 years can be found by growing the initial price ##(P_{\text{0, actual}})## forward.
###\begin{aligned} P_\text{100} &= P_{\text{0, actual}}.(1+r_\text{expected capital})^{100} \\ &= 1,000(1+0.15)^{100} \\ &= 1,174,313,451.70 \\ \end{aligned}###The net present value ##(V_0)## is the present value of the investment using the required total return ##(r_\text{required total}=0.1)##, subtracted by the initial price ##(P_{\text{0, actual}})##.
###\begin{aligned} NPV &= -\text{Cost} + \text{Benefit} \\ &= -P_{\text{0, actual}} + P_{\text{0, fair}} \\ &= -P_{\text{0, actual}} + \dfrac{P_\text{100}}{(1+r_\text{required total})^{100}} \\ &= -1,000 + \dfrac{1,174,313,451.70}{(1+0.1)^{100}} \\ &= -1,000 + 85,214.89624 \\ &= 84,214.89624 \\ \end{aligned}###Perpetual case
If the expected capital return is more than the required return forever, then the investment should have an infinite price and net present value.
###\begin{aligned} NPV &= -\text{Cost} + \text{Benefit} \\ &= -P_{\text{0, actual}} + P_{\text{0, fair}} \\ &= -P_{\text{0, actual}} + P_\text{0, actual} \left( \dfrac{1+r_\text{expected capital}}{1+r_\text{required total}} \right)^{\infty} \\ &= -1,000 + 1,000 \times \left( \dfrac{1+0.15}{1+0.1} \right)^{\infty} \\ &= -1,000 + 1,000 \times \infty \\ &= \infty \\ \end{aligned}###Note that an infinite price is impossible so the firm's claims about the 15% expected return lasting forever must be untrue.
Commentary: Actual and fair prices in the one hundred year case
These questions can be confusing because there appear to be two prices. Consider the one hundred year case. The current price of the investment offered by the firm is $1,000, let's call this the 'actual price'.
###P_\text{0, actual} = 1,000###The other price which is easily confused is the 'fair price', the price according to our calculations. This is the true or fundamental price that the investment should be worth, assuming that the firm's claims are true.
###\begin{aligned} P_\text{0, fair} &= \dfrac{P_\text{0, actual}.(1+r_\text{capital total})^{100}}{(1+r_\text{required total})^{100}} \\ &= \dfrac{1,000(1+0.15)^{100}}{(1+0.1)^{100}} \\ &= \dfrac{1,174,313,451.70}{(1+0.1)^{100}} \\ &= 85,214.89624 \\ \end{aligned}###Clearly, the actual $1,000 price offered by the firm selling the investment is too low compared to the fair price. The investment is under-priced, it has a positive alpha (or excess return) of 5% pa ##(=0.15-0.1)##, and that's why buying the investment is positive NPV.
###\begin{aligned} NPV &= -P_\text{0, actual} + P_\text{0, fair} \\ &= -1,000 + 85,214.89624 \\ &= 84,214.89624 \\ \end{aligned}###Question 780 mispriced asset, NPV, DDM, market efficiency, no explanation
A company advertises an investment costing $1,000 which they say is under priced. They say that it has an expected total return of 15% pa, but a required return of only 10% pa. Of the 15% pa total expected return, the dividend yield is expected to be 4% pa and the capital yield 11% pa. Assume that the company's statements are correct.
What is the NPV of buying the investment if the 15% total return lasts for the next 100 years (t=0 to 100), then reverts to 10% after that time? Also, what is the NPV of the investment if the 15% return lasts forever?
In both cases, assume that the required return of 10% remains constant, the dividends can only be re-invested at 10% pa and all returns are given as effective annual rates. The answer choices below are given in the same order (15% for 100 years, and 15% forever):
No explanation provided.