Question 48 IRR, NPV, bond pricing, premium par and discount bonds, market efficiency
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?
The NPV of buying any fairly priced asset is zero. Therefore the NPV of buying a fairly priced bond is also zero. Whether the bond is a premium or discount bond is irrelevant, it's unrelated to the NPV of buying it.
The fair price of a bond is the present value (PV) of its expected future cash flows, which is the present value of coupons and face value:
###\begin{aligned} P_\text{0, bond} &= PV(\text{coupons}) + PV(\text{face value}) \\ &= \frac{C_1}{r} \left(1 - \frac{1}{(1+r)^T} \right) + \frac{F_T}{(1+r)^T} \\ \end{aligned}###The net present value (NPV) of buying an asset is the present value of costs less gains.
###\begin{aligned} NPV &= -PV(\text{costs}) + PV(\text{gains}) \\ \end{aligned}###The cost of a bond is its price, and the gains from a bond are the coupons and face value. Since the price of a fairly priced bond equals the present value of the coupons and face value, then the net present value of buying a fairly priced bond must be zero.
Mathematically, we can re-arrange the bond price formula to be in the same form as the NPV formula, which shows that the NPV must be zero:
###P_\text{0, bond} = PV(\text{coupons}) + PV(\text{face value}) ### ###\underbrace{0}_{\text{NPV}} = -\underbrace{P_\text{0, bond}}_{PV(\text{costs})} + \underbrace{PV(\text{coupons}) + PV(\text{face value})}_{PV(\text{gains})} ###Note that premium bonds can also be fairly priced. The NPV of buying a fairly priced premium bond is zero. The term 'premium' does not indicate that the bond's price is above (or below) the fair price, it indicates that the bond's price is above its face value which is usually the $100 or $1,000 that's paid at maturity. Premium bonds have a higher price than their face value because the coupon rate is more than the total required return (the yield). Therefore investors are willing to pay a high price for the bond, higher than the face value, making the bond a premium bond. The highest price investors will pay for the bond will be the price that makes the NPV zero.
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 100 market efficiency, technical analysis, joint hypothesis problem
A company selling charting and technical analysis software claims that independent academic studies have shown that its software makes significantly positive abnormal returns. Assuming the 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) had mis-specification error so the returns may not be abnormal but rather fair for the level of risk.
Select the most correct response:
Charting and technical analysis uses past prices, or past returns which are based on past prices, to try to predict future prices and returns. According to the theory of weak form market efficiency, prices follow a random walk with a (small upward) drift and can not be predicted. The best estimate of tomorrow's price is the future value of today's price. The history of prices before today's price is irrelevant. For example, just because prices increased strongly in the past does not mean that they are expected to keep rising strongly in the future.
Positive abnormal returns are returns above the required return that investors deserve for the asset's level of systematic risk. The required return is generally found by using the CAPM or some other asset pricing model:
###r_\text{capm, i} = r_f + \beta_i (r_m - r_f)###The abnormal return is then the actual historical return less the required return:
###r_\text{abnormal, i} = r_\text{actual, i} - r_\text{capm, i}###If the charting software can consistently pick stocks with positive future abnormal returns then either weak for market efficiency is broken, or the market is weak form efficient but the CAPM is broken, or both!
In most markets, studies have shown that weak form efficiency holds. So prices follow a random walk and it is not possible to earn positive abnormal returns using past prices alone.
Note that according to the original theory by Eugene Fama, if weak-form market efficiency is broken, then all of the higher forms of market efficiency are also broken.
A person is thinking about borrowing $100 from the bank at 7% pa and investing it in shares with an expected return of 10% pa. One year later the person intends to sell the shares and pay back the loan in full. Both the loan and the shares are fairly priced.
What is the Net Present Value (NPV) of this one year investment? Note that you are asked to find the present value (##V_0##), not the value in one year (##V_1##).
The shares are expected to be worth $110 in one year, and the loan will be worth $107. So there is a positive expected cash flow of $3 in one year.
###\begin{aligned} V_1 &= V_\text{1, shares} - V_\text{1, loan} \\ &= V_\text{0, shares}(1+r_\text{shares})^1 - V_\text{0, loan}(1+r_\text{loan})^1 \\ &= 100(1+0.1)^1 - 100(1+0.07)^1 \\ &= 110 - 107 \\ &= 3 \\ \end{aligned} ###
Most people then discount the future value of $3 to get a present value of either $2.8037 or $2.7273 depending on whether they use a discount rate of 7 or 10% respectively. But this approach is wrong. The problem becomes apparent when trying to justify the use of one discount rate over another to find the present value of the $3. Should it be 10% or 7% or an average? Unfortunately this way of thinking was flawed from the beginning when the share's and loan's cash flows were added together because they have different risks and should be discounted by different required returns.
The way to analyse this question is to consider buying the shares and selling the loan separately. Note that 'borrowing' is the same thing as 'selling' a loan.
Since the shares are fairly priced, the NPV of buying them is zero. Similarly for the fairly priced loan, the NPV of selling it must be zero. So the NPV of the two transactions is zero plus zero which equals zero.
Alternatively, a more mathematical way of looking at it is that the expected returns of the fairly priced shares and loan are exactly equal to their respective discount rates. So they cancel out as follows:
###\begin{aligned} V_1 &= V_\text{1, shares} - V_\text{1, loan} \\ V_0 &= \frac{V_\text{1, shares}}{(1+r_\text{shares})^1} - \frac{V_\text{1, loan}}{(1+r_\text{loan})^1} \\ &= \frac{V_\text{0, shares}(1+r_\text{shares})^1}{(1+r_\text{shares})^1} - \frac{V_\text{0, loan}(1+r_\text{loan})^1}{(1+r_\text{loan})^1} \\ &= \frac{100(1+0.1)^1}{(1+0.1)^1} - \frac{100(1+0.07)^1}{(1+0.07)^1} \\ &= \frac{110}{(1+0.1)^1} - \frac{107}{(1+0.07)^1} \\ &= 100 - 100 \\ &= 0 \\ \end{aligned} ###
It seems nonsensical that there is a positive expected cash flow of $3 in one year, yet the NPV is zero. The reason why this scenario occurs in theory and in real life is that the expected value of the shares is $110 in one year but it could be a lot less. The loan, on the other hand, will definitely have $107 owing. In the worst case, after one year the shares become worthless (price = 0) and $107 is owed on the loan.
The expected gain of $3 is deserved for taking on the stock's higher level of systematic risk compared with the loan. Investors who suffer higher systematic risk deserve a higher return.
Other interesting view points about this scenario:
- In a risk-neutral world, all assets earn the risk-free rate thus there would be no positive expected future cash flow of $3. But in a risk-averse world, the $3 is compensation for taking on systematic risk.
- The principal of no-arbitrage says that in an efficient market it should be impossible to make unlimited risk-free gains. The portfolio of shares funded by the loan requires no capital so its payoff is unlimited, but the $3 expected gain is not risk-free. Thus the principal of no-(risk-free)-arbitrage holds.
- Banks prefer to lend with some form of security which has a value of more than the loan. The shares have the same value as the loan so they are unlikely to provide sufficient security. In the real world, margin loans on shares generally have a maximum debt-to-assets ratio of 0.7. Residential real estate lenders prefer borrowers to contribute a deposit of 20% of the house price, which equates to a debt-to-assets ratio of 0.8.
- An interesting line of research is the 'Kelly Criterion' and the 'Growth Optimal Portfolio'. The Kelly Criterion is widely known in the gambling literature and is used to calculate the optimal proportion of wealth to wager on a risky bet when the odds are in your favour. The Kelly criterion maximises the growth rate of wealth. It can also be applied to financial decisions such as this if the investor prefers to maximise her expected growth rate of wealth rather than her utility function which takes return and volatility into account.
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.
A very low-risk stock just paid its semi-annual dividend of $0.14, as it has for the last 5 years. You conservatively estimate that from now on the dividend will fall at a rate of 1% every 6 months.
If the stock currently sells for $3 per share, what must be its required total return as an effective annual rate?
If risk free government bonds are trading at a yield of 4% pa, given as an effective annual rate, would you consider buying or selling the stock?
The stock's required total return is:
Using the dividend discount model (DDM),
###\begin{aligned} P_{0} &= \frac{C_\text{6mth}}{r_\text{eff 6mth} - g_\text{eff 6mth}} \\ &= \frac{C_0(1+g_\text{eff 6mth})^1}{r_\text{eff 6mth} - g_\text{eff 6mth}} \\ \end{aligned} ### ###\begin{aligned} 3 &= \frac{0.14(1-0.01)^1}{r_\text{eff 6mth} - (-0.01)} \\ \end{aligned} ### ###\begin{aligned} r_\text{eff 6mth} &= \frac{0.14(1-0.01)^1}{3} - 0.01 \\ &= 0.0362 \\ \end{aligned} ### ###\begin{aligned} r_\text{eff annual} &= (1+r_\text{eff 6mth})^2-1 \\ &= (1+0.0362 )^2-1 \\ &= 0.07371044 \\ \end{aligned} ###Since this stock is very low risk, we can guess that it should have a low return close to the risk free rate which is the time value of money. Since this stock returns much more than the risk free rate (7.37% vs 4%), this stock is returning more than what we deserve. It is a good stock that we would like to buy. Its price is too low so it is under-priced, and buying it would have a positive NPV.
Note that this assumes that the stock's high historical rate of return in the past will continue into the future, but this might not be true.
Select the most correct statement from the following.
'Chartists', also known as 'technical traders', believe that:
Chartists make charts of past prices or returns and try to use them to extrapolate future prices or returns.
If a chartist can make consistent returns above what they deserve according to the systematic risk they take on, then they are breaking weak-form market efficiency, they are proving the random walk hypothesis wrong.
Most finance practitioners do not believe that chartists can make consistent positive abnormal returns. On the contrary, many expect that compared to a buy-and-hold strategy, most chartists would do worse since they simply rack up transaction costs with each trade where they sell a fairly priced stock and buy another fairly priced stock.
The idea of market efficiency in finance is very similar to competitive markets in economics. In the long run, firms operating in competitive markets with low barriers to entry will make zero economic profits. Note that economic profits include opportunity costs such as the cost of capital which accounting profit ignores.
Similarly, in the highly competitive financial markets it's very hard to make positive abnormal returns. If it was easy, someone would have already done it and bid the under-priced assets up and sold the over-priced assets down.
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.
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.
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.
Question 416 real estate, market efficiency, income and capital returns, DDM, CAPM
A residential real estate investor believes that house prices will grow at a rate of 5% pa and that rents will grow by 2% pa forever.
All rates are given as nominal effective annual returns. Assume that:
- His forecast is true.
- Real estate is and always will be fairly priced and the capital asset pricing model (CAPM) is true.
- Ignore all costs such as taxes, agent fees, maintenance and so on.
- All rental income cash flow is paid out to the owner, so there is no re-investment and therefore no additions or improvements made to the property.
- The non-monetary benefits of owning real estate and renting remain constant.
Which one of the following statements is NOT correct? Over time:
All statements are true except the last if the forecasts and assumptions are correct.
-
Statement a is true. Since the price ##(P)## is increasing by more than the net rent ##(C)## then the net rental yield ##(C_{t+1}/P_{t})## must fall and approach zero over time.
-
Statement b is true. The total required return on real estate ##(r_\text{real estate, total})## is the sum of the rental and capital yields.
###\begin{aligned} r_\text{real estate, total} &= r_\text{real estate, rent} + r_\text{real estate, capital} \\ &= \dfrac{C_1}{P_0} + \dfrac{P_1 - P_0}{P_0} \\ \end{aligned}###Since the price is and always will be fairly priced, and the rental yield approaches zero, then the total return must fall. The total yield will approach the capital yield.
-
Statement c is true. The total required return is based on the (systematic) risk of the investment, which is determined by the capital asset pricing model (CAPM). Since real estate is and always will be fairly priced, then real estate must plot on the CAPM's security market line (SML):
###\begin{aligned} r_\text{real estate, total} &= r_f + \beta_\text{real estate}.(r_m-r_f) \\ &= r_f + \beta_\text{real estate}.(r_\text{market risk premium}) \\ \end{aligned}###So for the required total return on real estate to fall ##(r_\text{real estate, total})##, either one or more of the risk free rate ##(r_f)##, market risk premium ##(r_\text{market risk premium} = r_m-r_f)##, or systematic risk as measured by beta ##(\beta_\text{real estate})## must fall.
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Statement d is true. Real estate comprises part of a country's wealth. If real estate prices grow by more than the country's wealth forever, then eventually real estate will become the only significant asset in the economy.
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Statement e is false . Rent comprises part of a country's gross domestic product (GDP). If rents grow by less than the country's GDP forever, then eventually rent will become insignificant compared to rest of the country's production. Rent will approach zero percent of the economy's production, not 100%.
Question 455 income and capital returns, payout policy, DDM, market efficiency
A fairly priced unlevered firm plans to pay a dividend of $1 next year (t=1) which is expected to grow by 3% pa every year after that. The firm's required return on equity is 8% pa.
The firm is thinking about reducing its future dividend payments by 10% so that it can use the extra cash to invest in more projects which are expected to return 8% pa, and have the same risk as the existing projects. Therefore, next year's dividend will be $0.90. No new equity or debt will be issued to fund the new projects, they'll all be funded by the cut in dividends.
What will be the stock's new annual capital return (proportional increase in price per year) if the change in payout policy goes ahead?
Assume that payout policy is irrelevant to firm value (so there's no signalling effects) and that all rates are effective annual rates.
The firm is fairly priced, so its required return (cost of capital) of 8% must equal its expected return (or internal rate of return). Since the new projects' risks are the same as the old projects, the required return must also be 8%.
###r_\text{total, new} = r_\text{total, old} = 0.08###The new projects' expected return is 8% too, so the new projects must be fairly priced, therefore they have a zero net present value. Another way of looking at this is that the cost of capital (total required return or deserved return) equals the internal rate of return (expected return) therefore the NPV is zero.
The share price must not change since the NPV of the projects is zero and there is no new money raised or paid by the firm. Also, payout policy is irrelevant to firm value. So the new share price ##P_{0, \text{new}}## must equal the old share price ##P_{0, \text{old}}##. The old 3% growth rate in the dividend must be equal to the old growth rate in the share price which is the old capital return ##P_\text{capital old}##, according to the theory of the perpetuity equation. Applying the perpetuity with growth formula:
###\begin{aligned} P_{0, \text{new}} &= P_{0, \text{old}} \\ &= \dfrac{C_\text{1 old}}{r_\text{total old} - r_\text{capital old}} \\ &= \dfrac{1}{0.08 - 0.03} \\ &= 20 \\ \end{aligned}###The new dividend ##C_\text{1 new}## will be only $0.90, so the new long term capital return in the perpetuity formula can be calculated:
###\begin{aligned} P_{0, \text{new}} &= \dfrac{C_\text{1 new}}{r_\text{total new} - r_\text{capital new}} \\ 20 &= \dfrac{0.9}{0.08 - r_\text{capital new}} \\ \end{aligned}### ###\begin{aligned} r_\text{capital new} &= 0.08 - \dfrac{0.9}{20} \\ &= 0.08 - 0.045 \\ &= 0.035 \\ \end{aligned}###This new 3.5% pa growth rate in the dividends is also the long term capital return of the stock. Therefore the stock price should increase 3.5% each year, faster than the old 3% pa rate. This makes sense since the firm is re-investing more money and should be able to generate higher growth in assets, dividends and the stock price.
Note that the instantaneous capital return is zero since there was no price-sensitive news released, just a change in payout policy. All of the new projects that will be invested in have zero NPV. So there is no reason for the stock price to increase straightaway.
Question 461 book and market values, ROE, ROA, market efficiency
One year ago a pharmaceutical firm floated by selling its 1 million shares for $100 each. Its book and market values of equity were both $100m. Its debt totalled $50m. The required return on the firm's assets was 15%, equity 20% and debt 5% pa.
In the year since then, the firm:
- Earned net income of $29m.
- Paid dividends totaling $10m.
- Discovered a valuable new drug that will lead to a massive 1,000 times increase in the firm's net income in 10 years after the research is commercialised. News of the discovery was publicly announced. The firm's systematic risk remains unchanged.
Which of the following statements is NOT correct? All statements are about current figures, not figures one year ago.
Hint: Book return on assets (ROA) and book return on equity (ROE) are ratios that accountants like to use to measure a business's past performance.
###\text{ROA}= \dfrac{\text{Net income}}{\text{Book value of assets}}###
###\text{ROE}= \dfrac{\text{Net income}}{\text{Book value of equity}}###
The required return on assets ##r_V## is a return that financiers like to use to estimate a business's future required performance which compensates them for the firm's assets' risks. If the business were to achieve realised historical returns equal to its required returns, then investment into the business's assets would have been a zero-NPV decision, which is neither good nor bad but fair.
###r_\text{V, 0 to 1}= \dfrac{\text{Cash flow from assets}_\text{1}}{\text{Market value of assets}_\text{0}} = \dfrac{CFFA_\text{1}}{V_\text{0}}###
Similarly for equity and debt.
The statement in answer A is untrue. The book value of equity would have grown from $100m to $119m (=100m + 29m - 10m) due to the addition of earnings and the subtraction of dividends.
The market value equity would be much higher due to the discovery of the valuable new drug which will increase the firm's future earnings and cash flows. This will cause a large increase in the share price, much higher than the $19m increase in book equity.
Notice that book equity is affected by events in the past, while market equity is only affected by what is expected to happen in the future. This is the fundamental difference between book (accounting) values and market (finance) values.
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}###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.
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 668 buy and hold, market efficiency, idiom
A quote from the famous investor Warren Buffet: "Much success can be attributed to inactivity. Most investors cannot resist the temptation to constantly buy and sell."
Buffet is referring to the buy-and-hold strategy which is to buy and never sell shares. Which of the following is a disadvantage of a buy-and-hold strategy? Assume that share markets are semi-strong form efficient. Which of the following is NOT an advantage of the strict buy-and-hold strategy? A disadvantage of the buy-and-hold strategy is that it reduces:
A disadvantage of a strict buy-and-hold strategy is that it prevents portfolio rebalancing which might restrict diversification. Portfolio rebalancing is the selling of stocks that you're over-exposed to since your weight in that stock or industry is too high, or selling stocks that you're under-exposed to.
Portfolio rebalancing avoids holding portfolios that are too concentrated in a single stock or industry. If a portfolio is not rebalanced then industry sectors that did well in the past can end up having a huge weight in the investment portfolio, reducing diversification and making the portfolio more risky.
For example in Australia, the mining and banking industries have done very well over the last few decades, while manufacturing has performed poorly. So a diversified portfolio formed 30 years ago that invested in the ASX200 market would be way overweight mining and banking now. This un-diversified portfolio would benefit from portfolio re-balancing.
All of the other points are valid advantages of a buy-and-hold strategy.
Question 776 market efficiency, systematic and idiosyncratic risk, beta, income and capital returns
Which of the following statements about returns is NOT correct? A stock's:
According to the CAPM, a stock's required total return depends on its systematic variance or beta. For some stock ##i##:
###r_\text{total i} = r_f + \beta_i (r_m - r_f)###A stock's total variance is the sum of the systematic and diversifiable variances. For some stock ##i##:
###\text{TotalVariance} = \text{SystematicVariance} + \text{DiversifiableVariance}### ###\begin{aligned} \sigma_\text{total i}^2 &= \sigma_\text{systematic i}^2 + \sigma_{\text{diversifiable i}}^2 \\ &= \beta_i^2\sigma_\text{m}^2 + \sigma_{\epsilon\text{ i}}^2 \\ \end{aligned}\\###Although the total return and total variance have the same title 'total', they are not closely related since total required returns depend on systematic variance only. This is because investors ignore diversifiable variance since it's easily reduced to zero by holding a variety of stocks.
The sum of the capital and dividend returns will equal the stock's total return.
###\begin{aligned} r_\text{total} &= r_\text{capital} + r_\text{dividend} \\ &= \dfrac{\text{Price}_\text{end} - \text{Price}_\text{start}}{\text{Price}_\text{start}} + \dfrac{\text{Dividend}_\text{end}}{\text{Price}_\text{start}} \\ \end{aligned}###The split between capital and dividend yields will depend on the company's payout policy. If the company chooses to:
- Not to pay any dividends and instead re-invests, the dividend yield will be zero and the capital yield will be high and equal to the total return.
- Pay out all of its cash flows as dividends, the dividend yield will be high and equal to the total return and the capital yield will be zero since there's no re-investment back into the company.
See Question 455 for a discussion of how dividend policy and re-investment affects capital returns.
Question 798 idiom, diversification, market efficiency, sunk cost, no explanation
The following quotes are most closely related to which financial concept?
- “Opportunity is missed by most people because it is dressed in overalls and looks like work” -Thomas Edison
- “The only place where success comes before work is in the dictionary” -Vidal Sassoon
- “The safest way to double your money is to fold it over and put it in your pocket” - Kin Hubbard
No explanation provided.
The famous investor Warren Buffett is one of few portfolio managers who appears to have consistently beaten the market. His company Berkshire Hathaway (BRK) appears to have outperformed the US S&P500 market index, shown in the graph below.
Read the below statements about Warren Buffett and the implications for the Efficient Markets Hypothesis (EMH) theory of Eugene Fama. Assume that the first sentence is true. Analyse the second sentence and select the answer option which is NOT correct. In other words, find the false statement in the second sentence.
If Buffett were an insider trader who illegally makes money from private information (which is not true, but suppose he is), this would provide evidence for rejecting the strong form EMH only, not the semi-strong form EMH.
Markets can still be semi-strong form efficient while insider traders are operating. This is because semi-strong form efficiency says that all public (not private) information is reflected in share prices. Strong form market efficiency says that all public and private information is reflected in stock prices.