Liam Rice
Chapter 4 (Problem Sets): 4, 5, 8, 16, 17, 19
Chapter 5 (Problem Sets): 4, 8, 9, 16, 18
4. Balanced funds, life-cycle funds, and asset allocation funds all invest in both the stock and
bond markets. What are the differences among these types of funds?
Balanced funds and asset allocation funds are a combination of stocks and bonds, but they differ
regarding their objectives. The purpose of asset allocation funds is to get consistent profits,
whereas, a balanced fund aims to achieve income and growth. Balanced funds retain share of the
investment in bonds, so their yield would be higher than that of asset allocation. These funds will
face a moderate risk level. Balanced funds are also funds that hold equity and fixed investment
securities in stable proportion. It is a combination of stock, bond, and money market
components. These are hybrid funds in one portfolio. An example of a balanced fund is lifecycle
fund, which is an asset mix of aggressive and conservative investors holding a wide variety of
stocks and bonds. Asset allocation is similar to balanced funds, as they also own stocks and
bonds, just not in equal proportion. Asset allocation is changed from time to time, based on the
performance Portfolio managers have the freedom to take the decision. Distribution of assets
depends upon forecasts by portfolio managers regarding the performance. Portfolio managers
have the freedom to make a decision. Allocation of assets depends upon forecasts by portfolio
relating to the performance of various markets. These funds are more focused on timings,
forecasting, and risks.
5. Why can closed-end funds sell at prices that differ from net asset value while open-end funds
do not?
Open-end funds are willing to buy back shares of the fund at net asset value from investors who
wish to “cash out” of the fund. In contrast, closed-end funds are not willing to redeem shares.
Investors in the closed-end fund who want to “cash out” must sell to another investor. The price
of shares of open-end funds does not diverge from net asset value because the fund stands ready
at all times to redeem an issue share of the dun at net asset value. It doesn’t make sense for
investors to buy and sell at a different price. Closed-end funds, however, do not redeem or issue
share other than the initial issue. Therefore, the price of shares of closed-end funds is not tied to
the net asset value and may diverge.
8. If the offering price of an open-end fund is $12.30 per share and the fund is sold with a
frontend load of 5%, what is its net asset value?
NAV = offering price * (1 – front-end load)
NAV = $12.30 * (1 -.05)
NAV = 12.30 * .95
NAV = $11.69
16. The New Fund had average daily assets of $2.2 billion last year. The fund sold $400 million
worth of stock and purchased $500 million during the year. What was its turnover ratio?
Total Stock sold = $400 million
Total stock held = $2,200 million
Turnover ratio = total stock sold / total assets held
Turnover ratio = $400 / $2,200
Turnover ratio = .1818 or 18.18%
17. If New Fund’s expense ratio (see the previous problem) was 1.1% and the management fee
was .7%, what were the total fees paid to the fund’s investment managers during the year? What
were other administrative expenses?
Fees paid to investment managers were .007 * $2.2 billion = $15.4 million
Since the total expense ratio was 1.1% and the management fee was .07%, we conclude that .
04% must be for other expenses. Therefore, other administrative expenses were: .004 * $2.2
billion = $8.8 million
19. Loaded-Up Fund charges a 12b-1 fee of 1.0% and maintains an expense ratio of .75%.
Economy Fund charges a front-end load of 2% but has no 12b-1 fee and an expense ratio of .
25%. Assume the rate of return on both funds’ portfolios (before any fees) is 6% per year. How
much will an investment in each fund grow to after: a. 1 year. b. 3 years. c. 10 years.
Assuming a hypothetical investment of $100.00:
A. Year 1 = 100 * (1 + .06 - .0175) = 104.25
B. Year 3 = 100 * (1 + .06 - .0175) ^3 = 116.30
C. Year 10 = 100 * (1 + .06 - .0175) ^10 = 151.62
Economy fund:
A. Year 1 = 100 * .98 * (1 + .06 - .0025) = 103.64
B. Year 3 = 100 * .98 * (1 + .06 - .0025) ^ 3 = 115.90
C. Year 10 = 100 * .98 * ( 1 + .06 - .0025) ^10 = 171.41
4. You have $5,000 to invest for the next year and are considering three alternatives: a. A money
market fund with an average maturity of 30 days offering a current yield of 6% per year. b. A 1-
year savings deposit at a bank offering an interest rate of 7.5%. c. A 20-year U.S. Treasury bond
offering a yield to maturity of 9% per year.
Money market funds are for short duration and offer minimum interest rate risk as return on
money market funds are not affected by changes in interest rate. So, the investor can invest
$5,000 in the money market fund now and when the interest rate increases the funds can be re-
invested in assets paying higher interest rates. One year saving deposits provide investors with
relatively fewer changes in interest rates. The alternative falls I the middle if terms of risk and
return trade-off. It offers higher return compared to money market fund but less degree of
interest rate risk compared to 20-year U.S. treasury bonds due to shorter maturity. The treasury
bond has the highest interest rate risk among all the three alternatives as it has the longest years
to maturity. An investor who forecasts the interest rates to fall in the long run will invest in 20-
year U.S. treasury bond as it will provide higher return in long-run
8. Derive the probability distribution of the 1-year HPR on a 30-year U.S. Treasury bond with an
8% coupon if it is currently selling at par and the probability distribution of its yield to maturity a
year from now is as follows: State of the Economy Probability YTM Boom .20 11.0% Normal
growth .50 8.0 Recession .30 7.0 For simplicity, assume the entire 8% coupon is paid at the end
of the year rather than every 6 months.
Holding period return = ending price of a share – beginning price + cash dividend / beginning
price
A 30-year US treasury bond was bought at par, so the price at the beginning is equal to the face
value of the bond that is $1,000. Therefore, the ending price is the price of the bond after a year
of time.
Coupon rate = .08
PMT = $80
Par value = $1,000
Maturity after a year = 29
State of Probability YTM Current Price Ending price HPR
economy
Boom .20 11.00% $1,000 $740.50 -17.95%
Normal .50 8.00 $1,000 $1,000.00 8.00%
Growth
Recession .30 7.00 $1,000 $1,122.78 20.28%
9. What is the standard deviation of a random variable q with the following probability
distribution: Value of q Probability 0 .25 1 .25 2 .50
√ p(s)[r(s)-E(r)] ^2=
= standard deviation
p(s) = probability
r(s) = holding period return
E(r) = mean return
E(r) = p(s) * r(s)
R(s) P(s) [p(s) * r(s)]
0 .25 0
1 .25 .25
2 .5 1
total E(r) = 1.25
P(S) R(S) E(R) [r(s) – E(r)] [r(s) – E(r)] [p(s)*[r(s)-
^2 E(r)]^2]
.25 0 1.25 -1.25 1.5625 .3906
.25 1 1.25 .25 .0625 .0156
.5 2 1.25 .75 .5625 .2813
Total = .6875
√ p(s)[r(s)-E(r)] ^2=
=√ .6875
=0.8292
16. You are faced with the probability distribution of the HPR on the stock market index fund
given in Spreadsheet 5.1 of the text. Suppose the price of a put option on a share of the index
fund with exercise price of $110 and time to expiration of 1 year is $12.
a. What is the probability distribution of the HPR on the put option?
State of Probability Ending HPR Ending HPR PUT
economy price value
Excellent .25 126.5 + 31.00% $0.00 -100% Out of
4.50 money
$131.00
good .45 110 + 4.00 14.00 0.00 -100 Out of
= 114.00 money
poor .25 89.75 + 3.5 -6.75 20.25 68.75 110 –
= 93.25 89.75
crash .05 46.00 -52.00 64.00 433.33 110 - 46
+2.00 =
48.00
b. What is the probability distribution of the HPR on a portfolio consisting of one share of the
index fund and a put option?
State of economy Probability Ending price + HPR
put + dividend
excellent .25 $131.00 [(131-112)/112 =
16.96%
Good .45 114.00 [(114 – 112) /
112] = 1.8
Poor .25 113.5 [(113.5-
112)/112] = 1.3
Crash .05 112.00 [(112-112)/112]
= 0.00
c. In what sense does buying the put option constitute a purchase of insurance in this case?
Buying the put option would guarantee the investor with a minimum HPR of 0.0% irrespective
of the fluctuations in the stock’s price. Therefore, it offers an insurance against decline in prices
18. Consider these long-term investment data: • The price of a 10-year $100 par zero coupon
inflation-indexed bond is $84.49. • A real-estate property is expected to yield 2% per quarter
(nominal) with a SD of the (effective) quarterly rate of 10%.
a. Compute the annual rate on the real bond.
b. Compute the CC annual risk premium on the real-estate investment.
c. Use the appropriate formula and Excel Solver or Goal Seek to find the SD of the CC annual
excess return on the real-estate investment.
d. What is the probability of loss or shortfall after 10 years?
A. Annual rate = In [ (face value / bond value) ^(1/n) – 1
Annual rate = In [ (100/84.49) (1/10) – 1
Annual rate = In [(1.183572) (.1) – 1
Annual rate = In [1.016997 – 1]
Annual rate = IN [(1 + .016997)]
Annual rate = .016854 or 1.69%
B. EAR = [ (1 + nominal rate) ^ - 1]
EAR = [ (1 + 2%)^4 – 1]
EAR = [ 1.08243 – 1]
EAR = .08243 or 8.24
EAR = In [(1 + rate)]
EAR = In [(1 + 8.24%)]
EAR = .07921 or 7.92%
Annual rate = In[(1+rate)]
Annual rate = In[(1 4%)]
Annual rate = .03922 or 3.92%
Annual risk premium = [EAR – annual rate]
Annual risk premium = [7.92% - 3.92%]
Annual risk premium (continuously compounding) = 4%
