FIN 310 Midterm Review (Problem Sets 1-4)

Both a call and a put currently are traded on stock XYZ. They both have a strike price of $50 and maturities of six months. a. What will be the profit to an investor who buys the call for $4 in the following scenarios for the stock price in six months? (i) $40 (ii) $45 (iii) $50 (iv) $55 (v) $60 b. What will be the profit in each scenario for an investor who buys the put for $6?

(The value of an option of expiration is 0 if it is out of the money, i.e. the strike is above the market price for a call, or below the market price for a put. In mathematical terms, if P is the market price and S is the strike price, then: Value of a call at expiration = max(0, P - S) Value of a put at expiration = max(0, S - P) in both cases assuming you own or are long the call or put. Doing the calculations: Long call for $4: Value of call at expiration Initial Cost Profit a. 0 4 -4 b. 0 4 -4 c. 0 4 -4 d. 5 4 1 e. 10 4 6 Long put for $6: Value of put at expiration Initial Cost Profit a. 10 6 4 b. 5 6 -1 c. 0 6 -6 d. 0 6 -6 e. 0 6 -6

You discover a treasure chest with $10 million in cash. Consider the following: Is this a real or a financial asset? Is society any richer for the discovery? Are you wealthier? Are your answers to the last two questions consistent? Is anyone worse off as a result of your discovery?

Cash is a financial asset because it is a claim on real assets, as it can be used to make purchases of goods and services as well as other financial assets. Society isn't richer. Financial assets don't increase the net wealth of society. When the government prints money, nothing happens. But when it is put into circulation, it is an asset to the holder and liability of the government or society as a whole. Yes, I am wealthier, as I have an asset, $10 million, that I can use to buy things. The answers are consistent. Financial assets net out, so my wealth is another's liability, my cash a claim on others. So I can be richer while society's wealth does not change. If the cash was already in circulation, then the asset (cash) and the liability (claim on government) already existed. Whoever owned the cash and lost it is worse off. If the cash was not in circulation--it fell off the truck from the Mint--then the government is worse off, but the financial assets and liabilities still net out to zero.

While browsing the web an ad flashes up for a course which promises to teach you how to make a fortune with no investment and no risk. You pass the ad by, or perhaps you click on it. Using concepts from the text/lectures, explain why.

Financial theory says such an opportunity cannot exist. Riskless profit with no investment is basically free money, like finding dollar bills in the street: they should already have been picked up. If it hadn't, it would be overwhelmed with takers, who would either exhaust the opportunity, or start bidding against each other until it was no longer free.

You invest in a portfolio and always reinvest any dividends and interest earned. Which of the following provides the best measure of the performance of that portfolio: dollar-weighted return geometric average return arithmetic return index return Why does it provide the best measure?

Generally the dollar-weighted average return or internal rate of return provides the most accurate measure of performance because it includes the impact of both compounding and the amount of funds in the portfolio. However, if the portfolio return numbers for each period are not simply based on price change, but include total returns--that is, both dividend and interest payments--then the dollar-weighted average return and the geometric average return should be the same. The arithmetic average is useful if you are trying to develop performance statistics for return and risk, but does not consider compounding, so is a poor measure of how an investor would fare over time if they reinvest their earnings or if they add and remove funds from time to time.

What features of money market securities distinguish them from other fixed income securities?

Money market securities are short-term, relatively low risk, and highly liquid. Also, their unit value almost never changes. The question asks you to distinguish money market securities from other fixed income securities. It would be a more complete answer to note that other fixed income securities are longer-term, tend to be higher risk as their price is more sensitive to changes in interest rates. Many are also highly liquid, though the further you get from Treasury securities generally the less liquid the market.

Explain the difference between a call option and a long position in a futures contract.

A call option conveys the right to buy the underlying asset at the exercise price. A long position in a futures contract carries an obligation to buy the underlying asset at the futures price. Both are "long" in the sense that if the underlying stock or commodity goes up in price, the holder profits. The profit of the call option holder is less, as they had to pay a premium to buy the option, whereas the futures contract was costless. But if the price goes down, the owner of the call option simply walks away, losing only the call premium paid for the option. The owner of the futures contract still has to buy the commodity at the agreed to price, presumably selling it at a loss (or unwind the contract by selling a matching future at the now lower price, realizing the same loss).

Suppose that short-term municipal bonds currently offer yields of 4%, while comparable taxable bonds pay 5%. Which gives you the higher after-tax yield if your tax bracket is: a. Zero b. 10% c. 20% d. 30%

After-tax yield = Rate on the taxable bond x (1 － Tax rate) a. The taxable bond. With a zero tax bracket, the after-tax yield for the taxable bond is the same as the before-tax yield (5%), which is greater than the 4% yield on the municipal bond. b. The taxable bond. The after-tax yield for the taxable bond is: 0.05 x (1 - 0.10) = 0.045 or 4.50%. c. Neither. The after-tax yield for the taxable bond is: 0.05 x (1 - 0.20) = 0.4 or 4%. The after-tax yield of taxable bond is the same as that of the municipal bond. d. The municipal bond. The after-tax yield for the taxable bond is: 0.05 x (1 - 0.30) = 0.035 or 3.5%. The municipal bond offers the higher after-tax yield for investors in tax brackets above 20%.

Explain what diversification is and why it is or is not desirable. Consider the problem discussed in the article from the perspective of a high net worth investor and using information from the text/lecture/article suggest how you would advise such a client.

Diversification requires you purchase a variety of assets with different risk and return characteristics. The article describes individuals who have tried to do that by buying a variety of investment funds. These investment funds aren't direct assets, but invest in other financial assets. It turns out the fund managers are all buying very similar assets. So when you "look through" the funds to the actual component assets, there is much less diversification than thought. An investors needs to consider the funds they are buying, and look through to the actual assets to see if they are actually diversifying their investments. They might be better diversified with fewer different funds; or with funds that clearly invest in distinct market segments.

According to the text the sum of all financial assets in the economy is exactly $0. Yet the more advanced the economy, the larger and more sophisticated the financial markets. Provide two reasons why financial markets are necessary and briefly explain them. In your explanation, also indicate potential problems with these justifications.

Financial markets make possible savings, permitting individuals to adjust consumption over their life. In advanced economies most people can't make all they need to live, and many move far from family who might support them. Financial markets permit them to save and invest for retirement or sickness. This added security permits individuals to take more risk and live more productive lives. On the other hand, they may save too much or too little, or misjudges the risks, or be overwhelmed by the complexity and invest badly. This can affect the economy as a whole and them personally. Financial assets permit the separation of ownership and management. This permits larger activities to be financed by using the resources of more individuals, and for professionals to run them. Developed economies have larger infrastructure projects, larger industries, etc., that could not be financed any other way. However, separating ownership and management can lead to agency problems, with managers helping themselves at the expense of the owners who hired them. Financial markets provide information about the relative value of real assets and help investors direct funds to their best use. It is not clear, however, that the information is always correct or that prices incorporate all available information, which could lead to incorrect pricing and misallocation. Financial markets help investors allocate risk to obtain the balance between risk and return that they feel best suits their needs. They can diversify to reduce risk, or concentrate their investments if they believe they have superior information and return/risk is mispriced. Of course, they can also be irrational or simply show poor judgement, and end up with unsuitable investments.

An expiring put option will be exercised and the stock will be sold if the stock price is below the exercise price. A stop-loss order causes a stock sale when the price falls below some limit. Compare and contrast the strategy of buying a put option to the strategy of issuing a stop loss order.

If you buy a put, then you will pay the premium. If the stock price stays above the strike price, you have a net loss of the premium. If the stock price falls below the strike, you will sell at the strike and could buy the stock back at the lower market, and, depending on how far the price falls, cover the put premium and make a cash profit. If you issue a stop-loss sell order to your broker, say at the same price as the strike on the put, then if the stock price stays above the stop-loss price nothing happens, and if it falls below the stock is sold at market. If the price is falling quickly, your broker may not be able to sell it at the desired price, so you may end up with less than you expected. If you get the stop-loss price then the profit profile looks like that of the put, but without having to have paid the premium. So the stop-loss looks like a superior strategy. But in a volatile market, the price may momentarily drop to the strike/stop-loss price and then rebound. If you issued a stop-loss order the stock would have been sold before you could pull the order. If you own a put, you have a choice whether to exercise, and when, up until the expiration date (at least for American options). So the premium you pay for the option does pay for something valuable: the ability to wait and see if the price is really moving down or just bouncing around a little.

Using data in the text, rank the following asset classes from lowest to highest average annual return over the period 1926 to 2013: Small stocks Long-term bonds Large stocks T-Bills Why would you expect the relative returns to be ordered in this way? How would you expect these assets to be ranked by a standard risk measure?

In order of increasing returns: T-Bills Long-term bonds. Large stocks Small stocks T-Bills are short-term and guaranteed by the US Government so should have the lowest returns. Long-term bonds pay a fixed interest rate and are issued by large firms, and so are a bit riskier but are not directly dependent on company performance. Stock returns depend on company performance, mainly growth and profits. But large companies are more stable than small one, so are likely to show smaller returns. One would expect risk, as measured by standard deviation or variance, to order the assets low to high the same way for the same reasons given above, as lower returns are generally associated with lower risk. If you reference the data in the text (if it's not in your answer it should be, but I will leave you to look it up in tables 5.2 and 5.3) the return and risk ordering are generally as just stated, but for some sub-periods there are exceptions.

Which of the following is the best measure of the market risk premium: -the difference between the return on an index fund and the return on Treasury bills -the difference between the return on a small-stock mutual fund and the S&P 500 index -the difference between the return on risky assets with the lowest returns and the return on Treasury bills -the difference between the highest and lowest yielding assets. Why?

The correct measure is the difference between the return on an index fund and T-Bills. The index fund represents the broad market, the available portfolio of risky assets. T-Bills are government guaranteed and short-term, so the return and the price are vey stable, risk free or nearly so. The difference tells you how much more you receive by investing in the market rather than staying safe, the definition of the risk premium. The other measures fall short in some way: -small stocks are a small part of the whole market; the S&P 500 is a broad measure but does not include small stocks; both are relatively risky. -it's not clear what risky assets with the lowest return measure, but again they would only be a portion of the market, not the whole. -highest and lowest yield assets would also not be representative of the market and are both risky.

You purchased 1,000 shares of Good Fund at the beginning of the year for $35 per share. There was a front-end load of 4%. The return on the assets in the fund was 15% over the course of the year. The fund's expense ratio was 1.2%. What is your rate of return over that first year? Suppose the return the second year is 12%. What is your annual rate of return over the two years?

The purchase totals 1000 x $35 = $35,000 but you lose 4% due to the front end load ($1400) so only have a position worth $33,600. (You could also assume you pay the $1400 in addition to the $35,000 for an initial investment of $36,400, but the math is messier.) With a return of 15%, at year end your investment is worth $33,600 x 1.15 = 38,640. You have to pay 1.2% in expenses. The worst case is to assume it is paid at year end (1.2% x $38,640 = $463.68), as the value increased, but it could be charged on average assets over the year, etc. Using this expense, you end the year with $38,640 - $463.68 = 38,176.32 on an initial investment of $35,000 for a return of 9.075% (end value divided by investment less 1). For two years: (1+12%)x$38,176.32 = $42,757.48 applying the 12% return. Expenses = 1.2% x $42,757.48 = $513.08 Ending value after expenses = $42,757.48 - 513.08 = $42,244.40 Two-year Return = $42,244.40/$35,000 - 1 = 20.7% One-year return is half the two year return or 10.35% If you don't like all the dollars, there is another way using only returns: The front-end load of 4% reduces your investment from 100% to 96% The first year return is 15%, less 1.2% for expenses, or 13.8%. 96% x (1+13.8%) = 108.48%, for a first year net return of 8.48% This last line assumes the 1.2% is applied evenly during the year. To be consistent with the analysis above, we apply 1.2% at the end: 96%x(1+15%)x(1-1.2%) = 109.075% for a first year net return of 9.075%. For the second year: Either 108.48% x (1+12%-1.2%) =120.19584%, or a 20.196% two year return, 10.098% simple annual average or 9.634% annual compound rate. or 109.075% x (1+12%) x (1-1.2%) = 120.698% or a 20.698% two year return, 10.349% simple annual average or 9.863% annual compound rate. Interesting you want the fee taken out at the end rather than taking it out of the period return

An investor invests 70% of their wealth in a risky portfolio with an expected rate of return of 15% and a variance of 5%, leaving the remaining amount in T-Bills, currently yield 1%. What is the expected return and standard deviation of this investor's portfolio?

The return will be 70% invested in the risky asset times the expected return of 15% plus 30% invested in T-Bills times the expected return of 1% or 70% x 15% + 30% x 1% = 10.8%. The standard deviation of the portfolio will be 70% of the standard deviation of the risky asset. The standard deviation of the risky asset is the square root of the variance of the risky asset. (The standard deviation of the TBill is assumed to be zero, so it has no impact.) So: 70% x sqrt(5%) = 15.6%.

FBN Corporation has just sold 100,000 shares of stock in an initial public offering. The underwriter's explicit fee was $70,000. The offering price was $50 per share. In trading after the offer closed, the share price jumped to $53. a. What is the cost to FBN of the IPO? b. What is the profit to the underwriter?

The trick here is to recognize there is both an explicit and an implicit cost. The explicit cost is the $70,000 fee. The implicit cost is the fact that the price rose shortly after the IPO. This suggest the stock could have been offered at the higher price and would have still sold out. The price increase was $3 per share (53-50), and there were 100,000 shares, so in some sense $300,000 was left "lying on the table". Who gets it? Certainly not the company. An underwriter buys the entire offer and then is responsible for selling it, taking any loss or profit, so could have made $300,000 in addition to the $70,000 fee. In reality, the underwrite would probably have promised some shares at the offer price to favored clients, and the sold the rest at a profit. BKM also notes the to compensate the underwriter for risk, the shares are sold to the underwriter by the firm at a small haircut, essentially a broker's fee, and additional revenue to the underwriter. So: (A) FBN can be said to have paid $70,000 and also lost $300,000 or so in foregone revenue, plus whatever the haircut from the IPO price. There would have been other costs like legal fees, travel for the roadshow, etc. (B) The underwriter earned $70,000 and some portion of the $300,000 in first day price increase, plus the commission/broker fee/haircut to the IPO price times the number of shares.. In reality it likely would not have gotten it all of the first day gain, depending on what it had promised customers. The underwriter would also have had expenses in preparing the deal, like lawyers, the salary to salesman who lined up customers, overhead, etc.

Financial firms have traditionally paid bond and equity traders with a share of the profits generated by their activity. Identify and define the primary concept in the text that applies to this situation and, using that concept, explain the possible advantages and disadvantages of this payment practice. Consider how the specific details of the payment practice might affect your answer.

This is an example of the agency problem: the firm wants the traders to act in the best interest of the firm. Incentive pay based on the profitability of their trading should encourage them to do that. However, return is related to risk. Some traders may take excessive risks in hope of high profits and a high bonus. Unfortunately, high risk may lead to big losses, and these are absorbed by the firm. The firm can mitigate this risk by paying the bonus based on average performance over a long time frame, longer than the time for the profit or loss of trading activity to be realized, and clawing back past bonuses if losses occur.

A T-bill with a face value of $10,000 and 87 days to maturity is selling at a bank discount ask yield of 3.4%. a. What is the price of the bill? b. What is its bond equivalent yield?

To get the discount off of face value we convert the annual bank discount ask yield to a discount factor for 87 days, noting the convention is to use a 360 day year, so: Discount Factor = Yield X Days to Maturity / Days in a year Bank discount of 87 days: 0.034 x (87 days/360 days) = 0.008217 a. Price is calculated by reducing the face value by the discount factor, or: Face x (1 - discount factor) = Price $10,000 x (1 - 0.008217) = $9,917.83 b. Bond equivalent yield = (Face value － Purchase price)/(Purchase price x Year Fraction) = ($10,000 － $9,917.83)/( $9,917.83 x (87 days 365 days) = 0.0348 or 3.48% This equation may be easier to understand as: BEY = ((Face - Purchase)/Purchase)X(365 days per year/ Number of days to maturity) Or, in numbers: 3.48% = (($10,000 - $9,917.83)/$9,917.83) x (365/87) Essentially, (Face-Purchase)/Purchase is the percentage return. Divide that by the number of days to maturity to get the daily rate of return (not compounded) and multiply by 365 to scale it up to a full year (again, on a non-compounded basis).

On January 1 you sold short 100 shares of SN Corp. stock at $23 per share. On March 1 the stock paid a dividend of $2.50 per share. On April 1 you covered the short sale by buying the stock at $18 per share. The broker commission for trading is $0.10 per share. What was your initial investment? What was your net return in dollars? What was the annualized return in percent?

To sell short you had to place 50% of the value in a margin account, or 50% x 100 x $23 = $1150. The short sale deposited an additional $2300 in your account which you can't withdraw, but which you did not contribute. The broker commission is $0.10 x 100 = $10. So your initial investment is $1160 and your account has $3450 in it. In March you had to cover the dividend, so 100 x $2.50 flowed out of your account to whomever loaned you the stock, reducing your account value to $3200. In April you bought 100 shares at $18 at a cost of $1800 plus another $10 in broker commissions, leaving you with $3200 - $1800 - $10 = $1390. Your net return in dollars is that ending value $1390, less your investment, $1160, or $230. The raw percentage return is $230/$1160 = 19.8%, but over a 3 month period, so on an annual basis it is four times that, or about 79%. As a check, note you made a $5 profit on the short of 100 shares, or $500, but you had to cover a $250 dividend payemnt and $10 commission twice, so a net dollar return of $230. (We ignore the cost of funds here: the $1160 investment had to come from somewhere. And in the real world, if the price rose while you held the short, you might have had to top up your margin to maintain the position. This sort of complication is beyond our analysis at this point, but very important in the real world.)

Explain the primary characteristics of the following types of investment funds: Unit Trusts Closed-end Funds Open-end Funds Exchange-traded Funds

Unit Trusts are pools of money invested in a portfolio that is fixed for the life of the fund. A reason that investors might find a Unit Trust appealing because they tend to invest in uniform types of investments and the composition for the trust is fixed as well. Unit Trusts also have little active management which also implies that the management fees can be lower than other managed funds. Investors might also want to avoid these funds because of the little amount of active management and the tendency to invest in uniform assets. This can mean that the performance of the trust is not being closely monitored and can result in significant losses if the assets decline in value, as well as the trust performing poorly as well if the specific asset class declines in value as well. Investors in Closed-end funds must sell the shares that they own to other investors in order to get out of a closed end fund. Shares are traded through organized exchanges and can be purchased through brokers as well. Investors might like this because the prices of the stock can be different than the NAV, which can mean that the prices can fluctuate differently and also cost less to investors who are looking to purchase stocks. Investors may not like this for the same reason as well. Also, they might not want to sell the shares that they currently own to other investors in order to get out of a closed end fund but they would have to if they look to terminate their position in the fund. Open end funds redeem or issue shares that are equal to their NAV. If investors wish to sell their shares, they are sold at the NAV instead of being sold off to other investors. Investors may like this because they are able to sell off shares that they own at the NAV for that stock and get capital in return, instead of selling them off to other investors like they would in a closed end fund. Investors may not like this because if they would like to get rid of the shares that they currently own, the NAV of that stock may be lower than what they initially bought it for, meaning that they are losing money. Exchange traded funds allow investors to invest in different index portfolios in the same way that they would a stock. Investors may like this because it may be easier to invest in a whole portfolio and less risky than just investing in separate stocks individually. A reason that investors may choose not to invest in ETFs is that they are linked to a specific index which can also have some risk attached if that index specifically were to preform poorly.

Suppose you want to do your financial analysis in real as opposed to nominal terms. What would you use for a risk-free asset?

You would want a short-term, government-guaranteed asset that is indexed for inflation. No such asset exists, so you would have to settle for assuming that the over the very short term inflation is close to zero, or you would have to create some asset with these characteristics by combining others. TIPS are longer term, so don't work, but can be used to get the expected inflation rate as the difference in yields between TIPS and comparable Treasuries will be a measure of the expected inflation rate (WHY?). Most analysts will subtract inflation from all returns to do historical analysis, and try to get an estimate of expected inflation for projections.

Look at the future listings for corn in figure 2.11 below. a. Suppose you buy one contract for December 2015 delivery. If the contract closes in December at a price of $3.95 per bushel, what will be your profit or loss? (Each contract calls for delivery of 5,000 bushels.) b. How many December 2015 maturity contracts are outstanding?

a. The December maturity futures price today is 388'2 or $3.8825 per bushel. If the contract closes at $3.95 per bushel in December, your profit / loss on each bushel will be the closing price you receive in December less the futures purchase you contracted for today, multiplied by the number of bushels per contract (for delivery of 5,000 bushels of corn) or: ($3.9500 - $3.8825) x 5000 = $ 337.50 gain.