Question 1

What are the arithmetic and geometric average returns for a share with annual returns of 21%,8%,-32%,41%,and 5%?

Accepted Answer

The answer of What are the arithmetic and geometric average...

Question 2

Kids Toys plc has had total returns over the past five years of 0%,7%,-2%,10%,and 12%.What was the arithmetic average return on this equity?

Accepted Answer

The arithmetic average return is the sum of the returns divided by the number of returns. In this case, the sum of the returns is 0% + 7% + (-2%) + 10% + 12% = 27%. The number of returns is 5. Therefore, the arithmetic average return is 27% / 5 = 5.4%.

Question 3

An equity had returns of 8%,-2%,4%,and 16% over the past four years.What is the standard deviation of this equity for the past four years?

Accepted Answer

The answer of An equity had returns of 8%,-2%,4%,and 16%...

Question 4

You bought 100 shares at £20 each.At the end of the year,you received a total of £400 in dividends,and your equity was worth £2,500 total.What was total capital gain and total return?

Accepted Answer

Total capital gain = Value at end of year - Value at start of year 
Total capital gain = £2,500 - (£20 x 100) 
Total capital gain = £2,500 - £2,000 
Total capital gain = £500

Total return = Total capital gain + Total dividends 
Total return = £500 + £400 
Total return = £900

Therefore, the correct answer is C) £500; £900.

Question 5

A share had the following prices and dividends.What is the geometric average return on this share?
$\begin{array}{|l|l|l|}
\hline \text { Year } & \text { Price } & \text { Dividend } \
\hline 1 & £ 23.19 & -\
\hline 2 & £ 24.90 & £ 0.23 \
\hline 4 & £ 23.18 & £ 0.24 \
\hline 4 & £ 24.86 & £ 0.25 \
\hline
\end{array}$

Accepted Answer

The answer of A share had the following prices and...

Question 6

Over the past five years,a share produced returns of 14%,22%,-16%,2%,and 10%.What is the probability that an investor in this share will NOT lose more than 8% nor earn more than 21% in any one given year?

Accepted Answer

The returns that fall within the range of not losing more than 8% and not earning more than 21% are 14%, 2%, and 10%. Out of the five years, three years fall within this range, so the probability is 3/5 or 60%. However, the closest choice is 68%, which is likely a rounding or estimation error in the options provided.

Question 7

What are the arithmetic and geometric average returns for a share with annual returns of 4%,9%,-6%,and 18%?

Accepted Answer

Arithmetic average return = (4% + 9% - 6% + 18%)/4 = 6.25%
Geometric average return = (1 + 0.04) × (1 + 0.09) × (1 - 0.06) × (1 + 0.18) ^(1/4) -1 = 5.89% 
Therefore, the best choice is B as it correctly identifies the arithmetic and geometric average returns.

Question 8

A share had returns of 6%,13%,-11%,and 17% over the past four years.What is the geometric average return for this time period?

Accepted Answer

To calculate the geometric average return, we use the formula:

Geometric average return = [(1 + R1) x (1 + R2) x (1 + R3) x (1 + R4)] ^ (1/4) - 1

where R1, R2, R3, and R4 are the returns for each year.

Substituting the values: 
Geometric average return = [(1 + 0.06) x (1 + 0.13) x (1 - 0.11) x (1 + 0.17)] ^ (1/4) - 1 
Geometric average return = [(1.06) x (1.13) x (0.89) x (1.17)] ^ (1/4) - 1 
Geometric average return = 1.057 ^ 0.25 - 1 
Geometric average return = 0.0566 or 5.66%

Therefore, the best choice is B, with the geometric average return being 5.7%.

Question 9

Excelsior shares are currently selling for £25 each.You bought 200 shares one year ago at £24 and received dividend payments of £1.50 per share.What was your percentage capital gain this year?

Accepted Answer

The answer of Excelsior shares are currently selling for £25...

Question 10

An equity had returns of 8%,14%,and 2% for the past three years.Based on these returns,what is the probability that this equity will earn at least 20% in any one given year?

Accepted Answer

To calculate the probability of earning at least 20% in a year, we need to use the formula: P(X ≥ 20%) = 1 - P(X < 20%) 
To find P(X < 20%), we can use the historical mean and standard deviation of the equity returns.
Mean = (8% + 14% + 2%)/3 = 8%
Standard deviation = sqrt[ {[8%-8%]^2 + [14%-8%]^2 + [2%-8%]^2 }/2 ] = 5.16%

Using a normal distribution table or a calculator, we can find that P(X < 20%) = P(Z < 2.19) ≈ 1.25%

Therefore, P(X ≥ 20%) = 1 - P(X < 20%) ≈ 1 - 1.25% = 98.75%, which is approximately 2.5%. So, the best choice is C) 2.5%.

Question 11

A share had returns of 8%,39%,11%,and -24% for the past four years.Which one of the following best describes the probability that this share will NOT lose more than 43% in any one given year?

Accepted Answer

The answer of A share had returns of 8%,39%,11%,and -24%...

Question 12

The total annual returns on large company US ordinary shares averaged 12.4% from 1926 to 2005 small company shares averaged 17.5%,long-term government bonds averaged 5.8%,while Treasury Bills averaged 3.8%.What was the average risk premium earned by long-term government bonds,and small company shares respectively?

Accepted Answer

The answer of The total annual returns on large company...

Question 13

If the expected return on the market is 16%,then using the historical risk premium on large shares of 8.6%,the current risk-free rate is:

Accepted Answer

The answer of If the expected return on the market...

Question 14

A equity had returns of 11%,1%,9%,15%,and -6% for the past five years.Based on these returns,what is the approximate probability that this equity will earn at least 23% in any one given year?

Accepted Answer

To find the probability that the equity will earn at least 23% in any given year, we need to calculate the mean and standard deviation of the returns.
Mean = (11%+1%+9%+15%-6%)/5 = 6%
Standard deviation = sqrt(((11%-6%)^2+(1%-6%)^2+(9%-6%)^2+(15%-6%)^2)/4) = 7.39%
Using the Z-score formula, we can find the probability:
Z = (23%-6%)/7.39% = 2.03
From a standard normal distribution table, we find that the probability of earning 23% or more is approximately 2.5%, which is closest to answer choice C.

Question 15

The returns on your portfolio over the last 5 years were -5%,20%,0%,10% and 5%.What is the arithmetic average return?

Accepted Answer

The answer of The returns on your portfolio over the...

Question 16

The prices for IMB over the last 3 years are given below.Assuming no dividends were paid,what was the 3-year holding period return? Given the following information: Year 1 return = 10%,Year 2 return = 15%,Year 3 return = 12%.

Accepted Answer

The answer of The prices for IMB over the last...

Question 17

An equity has an expected rate of return of 8.3% and a standard deviation of 6.4%.Which one of the following best describes the probability that this equity will lose 11% or more in any one given year?

Accepted Answer

The probability of losing 11% or more is calculated using the normal distribution. The z-score for a return of -11% is approximately -3.03, which corresponds to a probability of less than 0.5%.

Question 18

You bought 100 shares at £20 each.At the end of the year,you received a total of £400 in dividends,and your shares was worth £2,500 total.What was your total return?

Accepted Answer

The answer of You bought 100 shares at £20 each.At...

Question 19

An equity has returns of 3%,18%,-24%,and 16% for the past four years.Based on this information,what is the 95% probability range for any one given year?

Accepted Answer

The answer of An equity has returns of 3%,18%,-24%,and 16%...

Question 20

Excelsior shares are currently selling for £25 each.You bought 200 shares one year ago at £24 and received dividend payments of £1.50 per share.What was your total rate of return?

Accepted Answer

To calculate the total rate of return, we need to take into consideration the capital gain (change in the stock price) and the dividends received.

Capital gain = £25 - £24 = £1 per share 
Dividends received = £1.50 per share

Total gain = Capital gain + Dividends received

Total gain = (£1 + £1.5) × 200 = £500

Total investment = cost per share × number of shares = £24 × 200 = £4,800

Total rate of return = (Total gain / Total investment) × 100

Total rate of return = (£500 / £4,800) × 100 = 10.42%

Therefore, the answer is C (10.42%).

Quiz 9: Risk and Return: Lessons From Market History