Fight Finance

Question 14  bond pricing

For a price of $100, Andrea will sell you a 2 year bond paying annual coupons of 10% pa. The face value of the bond is $100. Other bonds with the same risk, maturity and coupon characteristics trade at a yield of 6% pa.

Would you like to the bond or politely ?

Question 54  NPV, DDM

A stock is expected to pay the following dividends:

Cash Flows of a Stock
Time (yrs)	0	1	2	3	4	...
Dividend ($)	0.00	1.15	1.10	1.05	1.00	...

After year 4, the annual dividend will grow in perpetuity at -5% pa. Note that this is a negative growth rate, so the dividend will actually shrink. So,

• the dividend at t=5 will be ##$1(1-0.05) = $0.95##,
• the dividend at t=6 will be ##$1(1-0.05)^2 = $0.9025##, and so on.

The required return on the stock is 10% pa. Both the growth rate and required return are given as effective annual rates.

What is the current price of the stock?

(a) $7.2968

(b) $7.5018

(c) $7.6667

(d) $7.7522

(e) $9.4101

Question 362  income and capital returns, DDM, real estate

Three years ago Frederika bought a house for $400,000.

Now it's worth $600,000, based on recent similar sales in the area.

Frederika's residential property has an expected total return of 7% pa.

She rents her house out for $2,500 per month, paid in advance. Every 12 months she plans to increase the rental payments.

The present value of 12 months of rental payments is $29,089.48.

The future value of 12 months of rental payments one year ahead is $31,125.74.

What is the expected annual capital yield of the property?

(a) -0.7814%

(b) -0.2724%

(c) 1.8124%

(d) 2%

(e) 2.1518%

Question 394  real option, option

According to option theory, it's rational for students to submit their assignments as or as possible?

Question 597  future, continuously compounding rate

A stock is expected to pay a dividend of $5 per share in 1 month and $5 again in 7 months.

The stock price is $100, and the risk-free rate of interest is 10% per annum with continuous compounding. The yield curve is flat. Assume that investors are risk-neutral.

An investor has just taken a short position in a one year forward contract on the stock.

Find the forward price ##(F_1)## and value of the contract ##(V_0)## initially. Also find the value of the short futures contract in 6 months ##(V_\text{0.5, SF})## if the stock price fell to $90.

(a) ##F_1=110.5171, V_0=0, V_\text{0.5, SF}=14.7829##

(b) ##F_1=110.5171, V_0=0, V_\text{0.5, SF}=15.1271##

(c) ##F_1=99.8244, V_0=0, V_\text{0.5, SF}=14.7829##

(d) ##F_1=99.8244, V_0=0, V_\text{0.5, SF}=20.5171##

(e) ##F_1=99.8244, V_0=0, V_\text{0.5, SF}=9.9144##

Question 628  CAPM, SML, risk

Assets A, B, M and ##r_f## are shown on the graphs above. Asset M is the market portfolio and ##r_f## is the risk free yield on government bonds. Assume that investors can borrow and lend at the risk free rate. Which of the below statements is NOT correct?

(a) Asset A has the same systematic risk as asset B.

(b) Asset A has more total variance than asset B.

(c) Asset B has zero idiosyncratic risk. Asset B must be a portfolio of half the market portfolio and half government bonds.

(d) If risk-averse investors were forced to invest all of their wealth in a single risky asset, so they could not diversify, every investor would logically choose asset A over the other three assets.

(e) Assets M and B have the highest Sharpe ratios, which is defined as the gradient of the capital allocation line (CAL) from the government bonds through the asset on the graph of expected return versus total standard deviation.

Question 756  bond pricing, capital raising, no explanation

A firm wishes to raise $50 million now. They will issue 5% pa semi-annual coupon bonds that will mature in 3 years and have a face value of $100 each. Bond yields are 6% pa, given as an APR compounding every 6 months, and the yield curve is flat.

How many bonds should the firm issue?

(a) 418,743

(b) 420,478

(c) 513,921

(d) 552,365

(e) 594,562

Question 779  mean and median returns, return distribution, arithmetic and geometric averages, continuously compounding rate

Fred owns some BHP shares. He has calculated BHP’s monthly returns for each month in the past 30 years using this formula:

###r_\text{t monthly}=\ln⁡ \left( \dfrac{P_t}{P_{t-1}} \right)###

He then took the arithmetic average and found it to be 0.8% per month using this formula:

###\bar{r}_\text{monthly}= \dfrac{ \displaystyle\sum\limits_{t=1}^T{\left( r_\text{t monthly} \right)} }{T} =0.008=0.8\% \text{ per month}###

He also found the standard deviation of these monthly returns which was 15% per month:

###\sigma_\text{monthly} = \dfrac{ \displaystyle\sum\limits_{t=1}^T{\left( \left( r_\text{t monthly} - \bar{r}_\text{monthly} \right)^2 \right)} }{T} =0.15=15\%\text{ per month}###

Assume that the past historical average return is the true population average of future expected returns and the stock's returns calculated above ##(r_\text{t monthly})## are normally distributed. Which of the below statements about Fred’s BHP shares is NOT correct?

(a) The returns ##r_\text{t monthly}## are continuously compounded monthly returns.

(b) The mean, median and mode of the continuously compounded annual return is expected to equal 0.8% per month.

(c) The annualised average continuously compounded return is ##\bar{r}_\text{cc annual}=12×0.008=0.096=9.6\%\text{ pa}##. The annualised standard deviation is ##\sigma_\text{annual} = \sqrt{12}×0.15=0.519615242 = 52\%\text{ pa}##.

(d) If the current price of the BHP shares is $20, they're expected to have a median value of $52.2339 ##(= 20×e^{0.008×12×10})## in 10 years.

(e) If the current price of the BHP shares is $20, they're expected to have a mean value of $13.5411 ##(= 20×e^{(0.008 - 0.15^2/2)×12×10})## in 10 years.

Question 831  option, American option, no explanation

Which of the following statements about American-style options is NOT correct? American-style:

(a) Options are always worth more than or equal to equivalent European-style options.

(b) Call options on dividend-paying stocks should sometimes be exercised just before the dividend.

(c) Put options on dividend-paying stocks should sometimes be exercised just after the dividend.

(d) Call options should be exercised now if the intrinsic option value ##(S-K)## is greater than the expected present value of the option’s future payoffs.

(e) Put options should be exercised now if the intrinsic option value ##(K-S)## is less than the expected present value of the option’s future payoffs.

Question 915  price gains and returns over time, IRR, NPV, income and capital returns, effective return

For a share price to double over 7 years, what must its capital return be as an effective annual rate?

(a) 9.9021%

(b) 9.9431%

(c) 10.4090%

(d) 28.5714%

(e) 100%