Book 3 Pages 52-100

Question 1

uncertainty of an investment’s realized (actual) rate of return will not equal its expected or forecasted rate of return

Answer 1

investment risk

Question 2

risk measured by standard deviation

Answer 2

total risk

Question 3

true or false? total risk includes both systematic risk and unsystematic risk

Answer 3

true

Risk Premium = Since systematic risk is non-diversifiable, investors demand a premium to make up for this risk factor. For instance, if a risk-free govt. security is giving a 5% return, then an investor expects to make more than that from the equity investment, like 8%. This difference of 3% (or a premium of 3%) is for assuming the systematic risk.

Question 4

true or false? total risk does not include diversifiable risk

Answer 4

false

Question 5

as more securities are added to the portfolio the level of unsystematic risk ____

Answer 5

decreases

Question 6

purchasing power risk is a ____ risk

Answer 6

systematic

Systematic risk includes market risk, interest rate risk, purchasing power risk, and exchange rate risk.

Purchasing power risk arises due to inflation. Inflation is the persistent and sustained increase in the general price level. Inflation erodes the purchasing power of money, i.e., the same amount of money can buy fewer goods and services due to an increase in prices. Therefore, if an investor’s income does not increase in times of rising inflation, then the investor is actually getting lower income in real terms. Fixed income securities are subject to a high level of purchasing power risk because income from such securities is fixed in nominal terms. It is often said that equity shares are good hedges against inflation and hence subject to lower purchasing power risk.

Question 7

reinvestment rate risk is a ____ risk

Answer 7

systematic

Question 8

financial risk is a ____ risk

Answer 8

unsystematic

Question 9

market risk is a ____ risk

Answer 9

systematic

Question 10

business risk is a ____ risk

Answer 10

unsystematic

Question 11

political risk is a ____ risk

Answer 11

unsystematic

Such type of risk occurs primarily due to political instability in a country or a region. For instance, if a country is at war, then the companies operating there would be considered risky.

The most narrow interpretation of an unsystematic risk is a risk unique to the operation of an individual firm. Examples of this can include management risks, location risks and succession risks.

EXAMPLE

Imagine a sector with three major firms in competition with one another: Firms A, B and C. Each is developing a new type of wind energy. Suppose all of these companies have effective business entrepreneurs at the helm.

However, a state government decides to subsidize Firm A or perhaps it prohibits a practice commonly used by Firms B and C that allegedly harms local bird populations. The stock value for Firm A tends to rise, while the stock value for the other two firms tends to fall.

Neither of these specific political or legal risk are inherent to the industry itself. Their negative effects are spread among select companies only. If an investor purchased stock in all three firms, he may be able to diversify away losses in Firms B and C via the gains from Firm A.

There are some political and legal risks that do affect entire industries in systematicways, however. It is not always possible to diversify away risks outside of the control of individual managers.

Question 12

tax risk is a ____ risk

Answer 12

unsystematic

Question 13

interest rate risk is a ____ risk

Answer 13

systematic

Question 14

exchange rate risk is a ___ risk

Answer 14

systematic

Question 15

default risk is a ___ risk

Answer 15

unsystematic

Question 16

investment manager risk is a ____ risk

Answer 16

unsystematic

Question 17

liquidity risk is a ____ risk

Answer 17

unsystematic

Question 18

risk that are inherited by investing in the market

Answer 18

systematic risks

Question 19

the risk the inflation will erode the real value of an investor’s assets

Answer 19

purchasing power risk

Question 20

the risk that proceeds available for reinvestment must be reinvested at a lower rate of return than that of the investment vehicle that generated the proceeds

Answer 20

reinvestment rate risk

Question 21

investments with longer terms to maturity have ____ reinvestment rate risk

Answer 21

greater

Question 22

are zero coupon bonds subject to reinvestment rate risk?

Answer 22

no

Question 23

are non-dividend paying stocks subject to reinvestment rate risk?

Answer 23

no

Question 24

the risk that changes in interest rates will affect the value of a security

Answer 24

interest rate risk

Question 25

as interest rates rise the value of a bond will ___

Answer 25

decrease

Question 26

true or false? rising interest rates usually have a positive effect on stocks

Answer 26

false

Question 27

the risk that a change in the relationship between the value of the dollar and the value of the foreign currency during the period of investment will negatively affect the investor’s return

Answer 27

exchange rate risk

Question 28

calculate an investors gain in the following scenario: John invests $1 million in ABC corp which is based in Mexico. The current exchange rate for pesos to dollars is 10 to 1. Jon sells his investment for 15 million pesos but the exchange rate has chanaged to 12 to 1.

Answer 28

John will get 15 million / 12 = $1,250,000 which is a $250,000 gain or 25% gain

Question 29

what does PRIME stand for in regards to systematic risk?

Answer 29

Purchasing power risk Reinvestment rate risk interest rate risk market risk exchange rate risk

Question 30

risk that is unique to a single security, business, industry, or country

Answer 30

unsystematic risk

Question 31

risk associated with the uncertainty of operating income

Answer 31

business risk

Question 32

the risk that a firm’s financial structure will negatively affect the value of an equity investment

Answer 32

financial risk

Question 33

true or false? if two firms have the same net income but one uses more debt than the other, the debt firm will have a higher return on equity

Answer 33

true

Question 34

the risk that a borrower will be unable to service its debt obligations

Answer 34

default risk

Question 35

true or false? default risk is also known as credit risk

Answer 35

true

Question 36

true or false? obligations of the US government are considered default risk free

Answer 36

true

Question 37

the risk that the political or economic climate of a country will negatively affect an investment

Answer 37

political risk

Question 38

the risk associated with the skills or philosophy of an individual manager of an investment fund or account

Answer 38

investment manager risk

Question 39

the ability to find a ready market where the investor may sell the investment

Answer 39

marketability

Question 40

the ability to sell an investment quickly and at a competitive price, with no loss of principal and little price concession

Answer 40

liquidity

Question 41

real estate is ____ but usually not ____

Answer 41

marketable ; liquid

Question 42

true or false? treasury bills are not liquid but they are marketable

Answer 42

false, they are both liquid and marketable

Question 43

money market accounts are liquid but not ___

Answer 43

marketable

Question 44

true or false? cash is the most liquid and marketable asset

Answer 44

true

Question 45

the risk that taxation of investment gains or losses will negatively affect investment return

Answer 45

tax risk

Question 46

the sum of observations divided by the number of observations

Answer 46

mean

Question 47

midpoint of the values after they have been ordered from smallest to largest

Answer 47

median

Question 48

the observation that appears with the greatest frequency

Answer 48

mode

Question 49

if the bell curve is skewed to the right (longer right tail) then this is called ______ skewness

Answer 49

positive

Question 50

which of the three averages (mean, median or mode) is greatest when there is positive skewness?

Answer 50

mean

Question 51

which of the three averages (mean, median, or mode) is greatest when there is negative skewness?

Answer 51

mode

Question 52

if the bell curve is skewed to the left (longer left tail) then this is called ____ skewness

Answer 52

negative

Question 53

measures if a distribution is more or less peaked than a normal distribution

Answer 53

Kurtosis

Question 54

when a distribution is more peaked than a normal distribution

Answer 54

leptokurtic

Question 55

when a distribution is less peaked than a normal distribution

Answer 55

playkurtic

Question 56

when more distributions are cluttered around the mean

Answer 56

leptokurtic

Question 57

true or false? investors who want to minimize volatility in their portfolios would prefer leptokurtic distributions

Answer 57

true

Question 58

when greater than 50% chance that an observation selected at random will fall on the left side of the mean

Answer 58

lognormal probability distribution

Question 59

lognormal distribution is skewed to the _____

Answer 59

right

Note that log-normal distributions are positively skewed with long right tails due to low mean values and high variances in the random variables.

Question 60

used to evaluate the risk associated with a given investment and assesses the impact of different variables on an investment’s returns

Answer 60

sensitivity analysis

Question 61

what two calculations do investors perform during sensitivity analysis?

Answer 61

NPV and IRR

NPV = Calculated as a present value of cash inflow less present value of cash outflow

• Expressed in form of currency return
• Absolute measure
• CAN be used to evaluate projects or investments where there are changes in cash flow
• NPV takes into account additional shareholders wealth for calculating the profitability of the project
• DISCOUNT RATE - if discount rate changes, NPV produces different results for the same project

IRR = Known as discount rate that make NPV of all cash inflows of a project equal to zero

• Expressed in the form of a percentage return a firm expects from a project
• Rate of return a project offers over its lifespan
• IRR Method cannot be used to evaluate projects where there are changing cash flows
• IRR doesn’t take into account additional shareholder’s wealth for calculating the profitability of the project
• DISCOUNT RATE - IRR produces same results even if the discount rate changes for the same project

EXAMPLE - IRR

1. Assume Company XYZ must decide whether to purchase a piece of factory equipment for $300,000. The equipment would only last three years, but it is expected to generate $150,000 of additional annual profit during those years. Company XYZ also thinks it can sell the equipment for scrap afterward for about $10,000. Using IRR, Company XYZ can determine whether the equipment purchase is a better use of its cash than its other investment options, which should return about 10%.
2. Here is how the IRR equation looks in this scenario:
   
   1. 0 = -$300,000 + ($150,000)/(1+.2431) + ($150,000)/(1+.2431)2 ($150,000)/(1+.2431)3 + $10,000/(1+.2431)4
3. The investment’s IRR is 24.31%, which is the rate that makes the present value of the investment’s cash flows equal to zero. From a purely financial standpoint, Company XYZ should purchase the equipment since this generates a 24.31% return for the Company –much higher than the 10% return available from other investments.
4. A general rule of thumb is that the IRR value cannot be derived analytically. Instead, IRR must be found by using mathematical trial-and-error to derive the appropriate rate. However, most business calculators and spreadsheet programs will automatically perform this function.

LIMITATIONS OF IRR

1. Also, IRR does not measure the absolute size of the investment or the return. This means that IRR can favor investments with high rates of return even if the dollar amount of the return is very small. For example, a $1 investment returning $3 will have a higher IRR than a $1 million investment returning $2 million. Another short-coming is that IRR can’t be used if the investment generates interim cash flows. Finally, IRR does not consider cost of capital and can’t compare projects with different durations.

Question 62

diversification and unsystematic risk have a ____ relationship

Answer 62

inverse (as diversification increases, unsystematic risk decreases

Question 63

term used to describe how adding an additional stock to a portfolio with only five stock will have a greater impact on the level of diversification than adding an additional stock to a portfolio of 30 stocks

Answer 63

law of diminishing returns

Question 64

measures the extent to which two variables move together

Answer 64

covariance

Question 65

how to calculate covariance

Answer 65

covariance = correlation x standard deviation of A x standard deviation of B

Question 66

calculate the correlation of the following assets: covariance = 0.0096 standard deviation of A = 20% standard deviation B = 12%

Answer 66

correlation = .40

Correlation = .0096 / (.20)(.12)

Question 67

measures the extent to which the returns on any two securities are related

Answer 67

correlation (R or p)

1. There are several types of correlation coefficients but the one that is most common is the Pearson correlation (r). This measures strength and direction of the linear relationship between two variables. It cannot capture nonlinear relationships between two variables and cannot differentiate between dependent and independent variables.
2. The strength of the relationship varies in degree based on the value of the correlation coefficient. For example, a value of 0.2 shows there is a positive relationship between the two variables, but it is weak and likely insignificant. Experts do not consider correlations significant until the value surpasses at least 0.8. However, a correlation coefficient with an absolute value of 0.9 or greater would represent a very strong relationship.

Question 68

true or false? correlation has a range of -1 to +1

Answer 68

true

Question 69

what does a correlation of -1 mean?

Answer 69

securities move in opposite directions

Question 70

what does a correlation +1 mean?

Answer 70

securities move in same direction

Question 71

what does a correlation of 0 mean?

Answer 71

securities are not related

Question 72

describes the percentage of variability of the dependent variable this is explained by changes in the independent variable

Answer 72

coefficient of determination (R squared)

1. The coefficient of determination is a measure used in statistical analysis that assesses how well a model explains and predicts future outcomes. It is indicative of the level of explained variability in the data set. The coefficient of determination, also commonly known as “R-squared,” is used as a guideline to measure the accuracy of the model.
2. Regardless of representation, an R-squared equal to 0 means that the dependent variable cannot be predicted using the independent variable. Conversely, if it equals 1, it means that the dependent of a variable is always predicted by the independent variable.
3. The goodness of fit, or the degree of linear correlation, measures the distance between a fitted line on a graph and all the data points that are scattered around the graph. The tight set of data will have a regression line that’s very close to the points and have a high level of fit, meaning that the distance between the line and the data is very small. A good fit has an R-squared that is close to 1.

Question 73

how do you calculate the coefficient of determination?

Answer 73

just square the correlation

Question 74

if the coefficient of determination = 1 then the portfolio has no _____ risk

Answer 74

unsytematic

In statistics, the percentage of a portfolio’s performance explainable by the performance of a benchmark index. The R square is measured on a scale of 0 to 100, with a measurement of 100 indicating that the portfolio’s performance is entirely determined by the benchmark index, perhaps by containing securities only from that index. A low R square indicates that there is no significant relationship between the portfolio and the index. An R Square is also called the coefficient of determination

Question 75

a relative measure of systematic risk

Answer 75

beta

• ​Beta coefficient(β)=Covariance(Re​,Rm​)​/Variance(Rm​)
  
  • Re​=the return on an individual stock
  • Rm=the return on the overall market
  • Covariance=how changes in a stock’s returns arerelated to changes in the market’s returns
  • Variance=how far the market’s data points spreadout from their average value​

The beta calculation is used to help investors understand whether a stock moves in the same direction as the rest of the market, and how volatile or risky it is compared to the market. For beta to provide any insight, the “market” used as a benchmark should be related to the stock. For example, calculating a bond ETF’s beta by using the S&P 500 as the benchmark isn’t helpful because bonds and stocks are too dissimilar.

In order to make sure stock is being compared to the right benchmark, it should have a high R-squared value in relation to the benchmark. R-squared is a statistical measure that shows the percentage of a security’s historical price movements that could be explained by movements in a benchmark index.

For example, a gold exchange-traded fund (ETF), such as the SPDR Gold Shares (GLD), is tied to the performance of gold bullion. Consequently, a gold ETF would have a low beta and R-squared in relation to the S&P 500, for example. When using beta to determine the degree of systematic risk, a security with a high R-squared value, in relation to its benchmark, would increase the accuracy of the beta measurement.

Question 76

the beta of the market is equal to ___

Answer 76

1

Question 77

if a security has a beta of 1.25 then the security is 25% ____ volatile than the market

Answer 77

more

Question 78

securities with a beta greater than 1 are known as a(n) ____ asset where as securities with a beta less than 1 are known as a(n) _____ assets

Answer 78

aggressive ; defensive

Question 79

formula for beta

Answer 79

Beta = Covariance / Variance

Covariance = Cov(x,y) = SUM [(xi - xm) * (yi - ym)] / (n - 1)

Divide Covariance by the two Standard Deviations to get the Correlation Coeffiicent.

Question 80

John’s investment had a return of 7.5% where as the market had a 9% return. The standard deviation of the investment and the market are 12% and 10% respectively. With a correlation of .65 between the investment and the market what is the beta?

Answer 80

.78

Question 81

a measure of risk or dispersion of outcomes around the mean or expected return

Answer 81

standard deviation

Question 82

approximately ____% of outcomes fall within 1 standard deviation of the mean

Answer 82

68%

Question 83

approximately ____% of outcomes fall within 2 standard deviation of the mean

Answer 83

95%

Question 84

approximately ___% of outcomes fall within 3 standard deviation of the mean

Answer 84

99%

Question 85

measures the number of standard deviations a data value is from the mean

Answer 85

z score

• A Z-score is a numerical measurement used in statistics of a value’s relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean. If a Z-score is 0, it indicates that the data point’s score is identical to the mean score. A Z-score of 1.0 would indicate a value that is one standard deviation from the mean. Z-scores may be positive or negative, with a positive value indicating the score is above the mean and a negative score indicating it is below the mean.

Question 86

how to find z score?

Answer 86

(data point - mean) / standard deviation

Question 87

if the data value is higher than the mean then the z score will be ____

Answer 87

postive

Question 88

what does a z score of 1.46 indicate

Answer 88

it means the data is 1.46 standard deviations above the mean

Question 89

if the data value is smaller than the mean then the z score will be___

Answer 89

negative

Question 90

true or false? standard deviation is a measure of total risk, systematic and unsystematic

Answer 90

true

Question 91

how to calculate variance

Answer 91

standard deviation squared

Question 92

calculate the standard deviation of the following portfolio: mean return = 12% security returns: 13.5% 12% 5% -2% 7% 23% 6% 10% 45% 10% .5% 14%

Answer 92

standard deviation = 12.29%

Question 93

true or false? if the securities standard deviation is greater than the market standard deviation the the security is more risky than the market

Answer 93

true

Question 94

calculate the expected rate of return for the following security: bull market = 30% probability with return of 50% slow growth = 45% probability with return of 10% bear market = 25% probability with return of -15%

Answer 94

= (.30 x .50) + (.45 x .10) + (.25 x -.15) = 15.75%

Question 95

only considers the downside volatility of an investment

Answer 95

semivariance

Question 96

money earned by investing a sum of money for a specific period

Answer 96

simple interest

Question 97

how to calculate simple interest

Answer 97

principal x interest rate x time

Question 98

calculate simple interest on the following: Johny borrows $1,000 for 2 years at 8%

Answer 98

1,000 x .08 x 2 = $160 (this is the interest only)

Question 99

calculate the compound interest on the following: johny invests $1,000 for 2 years at 8%

Answer 99

$1,000 x 1.08 x 1.08 = $1,166.40 or use pv = -$1,000 n = 2 i = 8

Question 100

how to calculate holding period return

Answer 100

(ending value - beginning value +/- cash flows) / beginning value

Question 101

calculate the holding period return on following: Bob purchases 100 shares of stock at $40 two years late he sells 100 shares at $52 in addition he received a dividends of $5 over the two years

Answer 101

42.5%

Question 102

calculate the Time Weighted Return on the following: Jim owns an investment with the following returns over the past 5 year period: 12% -9% 3% 5% -7%

Example

1. Year 1 = Buys 4 shares of stock with price of 65.20
   
   1. 260.80
2. Year 1 Dividend = 3.91
   
   1. 3.91 x 4 = 15.69
3. Year 1 Accumulation = Price is 72.37
   
   1. 72.37 x 4 = 289.48
4. FIRST Holding Period Return
   
   1. (289.48+16.64-260.8) / 260.8
5. Holding Period Return = 16.99%
6. Year 2 = Starting Price of 72.37
7. Year 2 = Buys 3 more shares of Stock
   
   1. 7 x 72.37 = 506.59
8. Year 2 = Dividend of 4.39
   
   1. 4.39 x 7 = 30.38
9. Year 2 Accumulaton = 78.16
   
   1. 7 x 78.16 = 547.12
10. 2nd Holding Period Return
    
    1. = (547.12 + 30.38 - 506.59) / 506.59
    2. = 13.99%

Time Weighted Rate of Return

• [(1.16994) x (1.13998)] ^1/2 - 1

Answer 102

[(1+12%) x (1-9%) x (1+3%) x (1+5%) x (1-7%)]^1/5 - 1 = 2.51%

Default way to compare Fund Managers

1. Treat Each Year as a stand-alone year
2. Holding Period Return for each year
3. Then we take the geometric average of these figures to find the average of these Holding Period Return
4. The TWR measure is often used to compare the returns of investment managers because it eliminates the distorting effects on growth rates created by inflows and outflows of money.

Question 103

IRR vs. TWR vs. Geometric Return

Answer 103

There are two main performance calculations: IRR, or Internal Rate of Return, and TWR, or Time Weighted Rate of Return.

IRR = The IRR measures how the portfolio’s investments did overall. It is a single rate of return that makes the value of everything added to the portfolio equal to everything taken out of the portfolio, or a constant rate of return that makes the present value of the portfolio’s ending value and all withdrawals precisely equal to the present value of the portfolio’s initial value and all contributions

1. IRR Calculation = The IRR cannot be computed directly. The IRR must be computed using a trial and error procedure in which you “guess” an answer, plug the guess into the equation, then modify the guess depending on the results. The new guess is plugged back into the equation, and the process is repeated until a satisfactory degree of precision is achieved. The initial “guess” made by Base Estimation Method, and the final number calculated through this iterative process.
2. Use When = Comparing the portfolio’s return to an overall goal. For example, use an IRR if you want to see if the portfolio is growing at least 10% in one year. The IRR return is affected by the size and timing of capital flows – larger flows affect the performance more than smaller flows. IRR is not suitable for determining the relative skill of an account manager or to be compared to a market index, as it is greatly affected by the size and timing of flows an investor decides to add to the portfolio

TWR = It removes the effect of the client’s decisions to deposit or withdraw money in the account. It measures investment performance (income and price changes) as a percentage of capital “at work,” effectively eliminating the effects of additions and withdrawals of capital and their timing that alter IRR accounting. Stated another way, TWR is designed to remove the effects of capital flows into and out of the portfolio.

1. TWR Calculation = [(1 + holding period 1 return) x (1 + holding period 2 return) x (1 + holding period 3 return) x …. -1] x 100
2. Use When = Reflects effects of the market and the manager’s choices over which investments to select for the portfolio. Eliminates effects of the size and timing of capital flows that alter IRR return numbers. Weights returns from each period equally no matter how much value is in the portfolio at the time. Comparing the growth of the portfolio to the market’s growth. For example, how did the portfolio perform as compared to a market index like the S&P 500? Comparing the performance of one portfolio manager to another. For example, if the investor moved assets under your management, but wanted to compare your performance to your predecessor

Geometric Mean = The main benefit of using the geometric mean is the actual amounts invested do not need to be known; the calculation focuses entirely on the return figures themselves and presents an “apples-to-apples” comparison when looking at two investment options over more than one time period. Geometric means will always be slightly smaller than the arithmetic mean, which is a simple average

1. Geometric Mean Calculation = Same as TWR Return but raised to the 1/nth power
   
   1. [(1 + holding period 1 return) x (1 + holding period 2 return) x (1 + holding period 3 return) x …. -1] x 100

Question 104

calculate the geometric mean of the following: returns: 15.2% 9.1% 6.5% 18.3% 16.8%

Answer 104

square root of the following: pv = -1 fv= 1.152 x 1.091 x 1.065 x 1.183 x 1.168 n = 5 pmt = 0 13.09%

OR

[(1 + r1) x (1 + r2) x (1 +rn) x … - 1]^1/n

Question 105

how to calculate the real rate of return

Answer 105

1 + nominal rate / 1 + inflation minus 1 x 100

Question 106

calculate the real rate of return of the following: nominal return = 10% infaltion = 4%

Answer 106

5.77%

Real Rate of Return = (1 + Nominal Rate) / (1 + Inflation Rate) - 1

Real Rate of Return = 1.10 / 1.04 - 1

Real Rate of Return = .0577%

Question 107

if a lender advertises a 1.25% monthly rate what is the APR?

Answer 107

1.25% x 12 = 15%

An annual percentage rate (APR) is the annual rate charged for borrowing or earned through an investment. APR is expressed as a percentage that represents the actual yearly cost of funds over the term of a loan. This includes any fees or additional costs associated with the transaction but does not take compounding into account.

Question 108

provides the annual rate of interest of an investment or debt when compounding occurs more than once per year

Answer 108

effective annual rate

Question 109

how to calculate effective annual rate

Union Bank offers a nominal interest rate of 12% on its certificate of deposit to Mr. Obama, a bank client. The client initially invested $1,000 and agreed to have the interest compounded monthly for one full year

Answer 109

EAR = [1 + (i / n)] ^n - 1

As a result of compounding, the effective interest rate is 12.683%, in which the money grew by $126.83 for one year, even though the interest is offered at only 12%.

End Mode

12 P/Y

PV = -1.000

N = 12

I% Year = 12%

Fv = 1,126.83

THEN

1,126.83/1,000 = 1.12683 - 1 = .12683 * 100 = 12.683%

Question 110

calculate the EAR on the following: Johnny carries a balance on his credit card. The nominal APR is 9.99% compounded daily

Answer 110

[1+ (.0999 / 365)] ^365 - 1 10.5%

Question 111

the earnings rate at which the present value of a series of cash flows will equal its cost

Answer 111

IRR

Question 112

the geometric annual rate of return measured on the basis of the current year value of the asset

Answer 112

time weighted return

Question 113

measures the rate of return without considering an investor’s size or timing of funds

Answer 113

time weighted return= [(1 + Holding Period Return₁) * (1 + Holding Period Return₂) * (Holding Period Return₃)]^1/3 - 1

• Geometric mean, sometimes referred to as compounded annual growth rate or time-weighted rate of return, is the average rate of return of a set of values calculated using the products of the terms.
• The time-weighted return (TWR) multiplies the returns for each sub-period or holding-period, which links them together showing how the returns are compounded over time.
• The time-weighted return (TWR) helps eliminate the distorting effects on growth rates created by inflows and outflows of money.

Scenario 1

1. Investor 1 invests $1 million into Mutual Fund A on December 31.
2. On August 15 of the following year, his portfolio is valued at $1,162,484.
3. At that point (August 15), he adds $100,000 to Mutual Fund A, bringing the total value to $1,262,484.
4. By the end of the year, the portfolio has decreased in value to $1,192,328. The holding-period return for the first period, from December 31 to August 15, would be calculated as:
   
   1. Holding Period Return = ($1,162,484 - $1,000,000) / $1,000,000 = 16.25%
5. The holding-period return for the second period, from August 15 to December 31, would be calculated as:
   
   1. Holding Period Return = ($1,192,328 - ($1,162,484 + $100,000)) / ($1,162,484 + $100,000) = -5.56%
6. The time-weighted return for the two time periods is calculated by multiplying each subperiod’s rate of return by each other. The first period is the period leading up to the deposit, and the second period is after the $100,000 deposit.
   
   1. Time-weighted return = (1 + 16.25%) x (1 + (-5.56%)) - 1 = 9.79%
   2. TWR = [(1.1625) x .(9444) - 1] x 100
   3. TWR = [1.0979 - 1] x 100
   4. TWR = 9.79%

Scenario 2

1. Investor 2 invests $1 million into Mutual Fund A on December 31.
2. On August 15 of the following year, her portfolio is valued at $1,162,484. At that point (August 15), she withdraws $100,000 from Mutual Fund A, bringing the total value down to $1,062,484.
3. By the end of the year, the portfolio has decreased in value to $1,003,440.
4. The holding-period return for the first period, from December 31 to August 15, would be calculated as:
   
   1. Holding Period Return = ($1,162,484 - $1,000,000) / $1,000,000 = 16.25%
5. The holding-period return for the second period, from August 15 to December 31, would be calculated as:
   
   1. Holding Period Return = ($1,003,440 - ($1,162,484 - $100,000)) / ($1,162,484 - $100,000) = -5.56%
6. The time-weighted return over the two time periods is calculated by multiplying or geometrically linking these two returns:
   
   1. Time-weighted return = (1 + 16.25%) x (1 + (-5.56%)) - 1 = 9.79%

Question 114

the compounded annual rate of return (IRR) that discounts a portfolio’s future value and cash flows to a present value

Answer 114

dollar weighted return

Question 115

what is the preferred method for analyzing the performance of a portfolio manager?

Answer 115

time weighted return

Question 116

how do you calculate the tax-adjusted rate of return?

Answer 116

rate of return x (1 - tax rate)

Question 117

represents the return for a set of securities, such as a portfolio, where each return is weighted by the proportion of the security to the entire group or portfolio

Answer 117

weighted average return

Question 118

refers to changing the mix of investment classes based on changing market conditions

Answer 118

tactical asset allocation

Question 119

true or false? when using a tactical asset allocation there is a greater chance to experience high transaction costs

Answer 119

true

Question 120

true or false? tactical asset allocation is also known as market timing

Answer 120

true

Question 121

an investment strategy investing in both broad market indexes and higher-risk alternatives

Answer 121

core and satellite

Question 122

a portfolio that has the highest amount of return for a given level of risk

Answer 122

efficient portfolio

Question 123

who is said to have come up with Modern Portfolio Theory

Answer 123

Harry Markowitz

Question 124

what does the efficient frontier highlight?

Answer 124

the efficient frontier shows the portfolios that provide the highest rate of return for a given risk or the portfolios with the lowest risk for a given rate of return

Question 125

what is the indifference curve?

Answer 125

graph used to measure the risk reward trade offs an investor is willing to make

Question 126

the portfolio that lies at the ____ of the indifference curve and the efficient frontier is the optimum portfolio for the investor

Answer 126

tangent

Question 127

true or false? Portfolios above the efficient frontier are attainable

Answer 127

false

Question 128

the x axis of the efficient frontier measures ___

Answer 128

risk

Question 129

the y axis of the efficient frontier measures ___

Answer 129

expected portfolio return

Question 130

who developed the CAPM?

Answer 130

William Sharpe

Question 131

how to calculate CAPM?

Answer 131

rf + beta (market return - rf) = expected rate of return

Question 132

what does CAPM calculate?

Answer 132

expected rate of return

Question 133

appears in the capital asset pricing model to depict the rates of return for efficient portfolios subject to the risk level (standard deviation) for a market portfolio and the risk-free rate of return.

Answer 133

capital market line

Question 134

represents some portion of the portfolio is invested in the market portfolio and the remainder is invested in risk free government securities

Answer 134

the lending portfolio

Question 135

the lending portfolio is located to the ___ of the market portfolio on the CML

Answer 135

left

Question 136

represents in investor putting 100% of investment assets in the market portfolio and has borrowed funds at the risk free rate to invest in the market portfolio

Answer 136

borrowing portfolio

• The line slopes up and to the right from the point in the middle. Every point on the right half of the line represents a borrowing portfolio. This shows how an investor can buy the market portfolio, and also borrow money in order to buy more of the market portfolio. Therefore, an investor can hold the same market portfolio and increase his risk and expected return. Notice that the slope of the lending portfolio is higher than that of the borrowing portfolio. This is because the rate at which one can borrow money will always be higher than the risk free lending rate.

Lending Portfolio

• The line slopes down and to the left from this point. All of the points on this left half of the line represent a lending portfolio. A lending portfolio consists of the market portfolio, plus some risk free government securities. These securities serve to reduce the risk profile of the portfolio, while of course also reducing expected returns.

Question 137

the borrowing portfolio is located to the _____ of the market portfolio on the CML

Answer 137

right

Question 138

how to calculate the CML

Answer 138

Portfolio Return = Risk Free Rate + ((Market Return - Risk Free Rate)/Standard Dev of Market Returns) x Standard Dev of Portfolio Return

Question 139

true or false? the CML uses standard deviation as a risk measure

Answer 139

true

CML differs from the more popular efficient frontier in that it includes risk-free investments. The intercept point of CML and efficient frontier would result in the most efficient portfolio, called the tangency portfolio.

The CML is sometimes confused with the security market line (SML). The SML is derived from the CML. While the CML shows the rates of return for a specific portfolio, the SML represents the market’s risk and return at a given time, and shows the expected returns of individual assets. And while the measure of risk in the CML is the standard deviation of returns (total risk), the risk measure in the SML is systematic risk, or beta. Securities that are fairly priced will plot on the CML and the SML. Securities that plot above the CML or the SML are generating returns that are too high for the given risk and are underpriced. Securities that plot below CML or the SML are generating returns that are too low for the given risk and are overpriced.

Question 140

true or false? the SML uses beta as a measure of risk

Answer 140

true

Question 141

how to calculate SML

Answer 141

same way as CAPM

E(r) = R_f + Risk Premium

1. Market Risk Premium = (R_m - R_f)
2. Risk Premium = B(R_m - R_f)

NOTE = CML is measured with expected return and standard deviation as x axis. Concerned with actual efficient portfolios

SML / CAPM = specific securities, which is measured with expected return and Beta as the x axis. Market Portfolio has a Beta of 1.0.

Question 142

true or false? CAPM explains the returns on stock as a result of one factor

Answer 142

true

Question 143

attempts to explain the portfolio return in terms of multiple factors

EXAMPLE - APT

1. For example, the following four factors have been identified as explaining a stock’s return and its sensitivity to each factor and the risk premium associated with each factor have been calculated:
   
   1. Gross domestic product (GDP) growth: ß = 0.6, RP = 4%
   2. Inflation rate: ß = 0.8, RP = 2%
   3. Gold prices: ß = -0.7, RP = 5%
   4. Standard and Poor’s 500 index return: ß = 1.3, RP = 9%
   5. The risk-free rate is 3%

Answer 143

arbitrage pricing theory

Arbitrage pricing theory (APT) is a multi-factor asset pricing model based on the idea that an asset’s returns can be predicted using the linear relationship between the asset’s expected return and a number of macroeconomic variables that capture systematic risk. It is a useful tool for analyzing portfolios from a value investing perspective, in order to identify securities that may be temporarily mispriced.

The Formula for the Arbitrage Pricing Theory Model Is:

1. E(R)_i​ = E(R)_z​ + (E(I) − E(R)_z​) × β_n​
   
   1. E(R)_i​ = Expected return on the asset
   2. R_z​ = Risk-free rate of return
   3. β_n = Sensitivity of the asset price to macroeconomic factor n
   4. E_i = Risk premium associated with factor i​

The arbitrage pricing theory was developed by the economist Stephen Ross in 1976, as an alternative to the capital asset pricing model (CAPM)

APT:

1. Expected return = 3% + (0.6 x 4%) + (0.8 x 2%) + (-0.7 x 5%) + (1.3 x 9%) = 15.2%

Question 144

this theory suggests that investors are unable to outperform the market on a consistent basis without accepting additional risk

Answer 144

efficient market hypothesis

Question 145

states that the current stock prices reflect all available information for a company and that the prices rapidly adjust to reflect any new information

Answer 145

efficient market hypothesis

Question 146

true or false? the efficient market hypothesis and technical analysis directly contradict each other

Answer 146

true

Question 147

holds that the current stock prices have already incorporated all historical data, such as prices, trading volume, and published financial info

Answer 147

efficient market hypothesis weak form

1. The weak form suggests that today’s stock prices reflect all the data of past prices and that no form of technical analysis can be effectively utilized to aid investors in making trading decisions.
2. The semi-strong form efficiency theory follows the belief that because all information that is public is used in the calculation of a stock’s current price, investors cannot utilize either technical or fundamental analysis to gain higher returns in the market.
3. The strong form version of the efficient market hypothesis states that all information – both the information available to the public and any information not publicly known – is completely accounted for in current stock prices, and there is no type of information that can give an investor an advantage on the market.

Question 148

holds that the current stock prices not only reflect all past historical data but also data from analyzing current financial statements, industry and economic outlooks

Answer 148

efficient market hypothesis semi-strong form

Question 149

Criticism of EMH

Answer 149

1. Investors, including the likes of Warren Buffett and researchers have disputed the efficient-market hypothesis both empirically and theoretically.
2. Behavioral economists attribute the imperfections in financial markets to a combination of cognitive biases such as
   
   1. overconfidence,
   2. overreaction,
   3. representative bias,
      
      1. 2. In financial markets, one example of this representative bias is when investors automatically assume that good companies make good investments. However, that is not necessarily the case. A company may be excellent at their own business, but a poor judge of other businesses.
   4. information bias, and
   5. various other predictable human errors in reasoning and information processing.
3. These have been researched by psychologists such as Daniel Kahneman, Amos Tversky and Paul Slovic and economist Richard Thaler. These errors in reasoning lead most investors to avoid value stocks and buy growth stocks at expensive prices, which allow those who reason correctly to profit from bargains in neglected value stocks and the overreacted selling of growth stocks.[citation needed]
4. Empirical evidence has been mixed, but has generally not supported strong forms of the efficient-market hypothesis. According to Dreman and Berry, in a 1995 paper, low P/E stocks have greater returns.

PRO Efficient Market Theorists - Ray Ball that these higher returns could be attributed to higher beta, whose research had been accepted by efficient market theorists as explaining the anomaly in neat accordance with modern portfolio theory.

Question 150

what type of info is reflected in weak form of EMH?

Answer 150

Weak form efficiency doesn’t consider technical analysis to be accurate and asserts that even fundamental analysis, at times, can be flawed. It’s therefore extremely difficult, according to weak form efficiency, to outperform the market, especially in the short term

Weak form efficiency claims that past price movements, volume and earnings data do not affect a stock’s price and can’t be used to predict its future direction. Weak form efficiency is one of the three different degrees of efficient market hypothesis (EMH).

EXAMPLE

• Similarly, let’s assume Apple Inc. (APPL) has beaten analysts’ earnings expectation in the third quarter consecutively for the last five years. Jenny, a buy-and-holdinvestor, notices this pattern and purchases the stock a week before it reports this year’s third quarter earnings in anticipation of Apple’s share price rising after the release. Unfortunately for Jenny, the company’s earnings fall short of analysts’ expectations. The theory states that the market is weakly efficient because it doesn’t allow Jenny to earn an excess return by selecting the stock based on historical earnings data.

Example

• Suppose David, a swing trader, sees Alphabet Inc. (GOOGL) continuously decline on Mondays and increase in value on Fridays. He may assume he can profit if he buys the stock at the beginning of the week and sells at the end of the week. If, however, Alphabet’s price declines on Monday but does not increase on Friday, the market is considered weak form efficient.

Question 151

what type of info is reflected in semi-strong form of EMH?

Answer 151

technical and fundamental analysis

Question 152

what type of info is reflected in strong form of EMH?

Answer 152

technical analysis, fundamental analysis, and insider info

In strong-form efficiency, share prices reflect all information, public and private, and no one can earn excess returns.

If there are legal barriers to private information becoming public, as with insider trading laws, strong-form efficiency is impossible, except in the case where the laws are universally ignored.

To test for strong-form efficiency, a market needs to exist where investors cannot consistently earn excess returns over a long period of time. Even if some money managers are consistently observed to beat the market, no refutation even of strong-form efficiency follows: with hundreds of thousands of fund managers worldwide, even a normal distribution of returns (as efficiency predicts) should be expected to produce a few dozen “star” performers.

Question 153

suggests that higher returns are attainable with portfolios consisting of securities with low P/E ratios

Answer 153

P/E effect

Question 154

states that stocks have a tendency to decline in value during the month of December and to move up in January

Answer 154

January effect

Question 155

states that with fewer analysts following a stock there could be stocks that are over/under valued

Answer 155

small firm effect

Question 156

give an example of using a collar in terms of options

Answer 156

writing a call option in order to generate premium to pay for a put option

Question 157

allows an un-diversified portfolio to be exchanged for interest in a diversified portfolio

Answer 157

exchange fund (not an ETF)

• Because an investor swaps shares with the fund, no sale actually occurs. This allows the investor to defer the payment of capital gains tax until he or she sells the fund’s units.

An exchange fund (also known as a “swap fund”) is a stock fund that allows an investor to exchange his or her large holding of a single stock for units in a portfolio. Exchange funds provide investors with an easy way to diversify their holdings while deferring any taxes from capital gains

Exchanged funds may require the potential participants to have a minimum liquidity of $5 million cash in order to join and contribute.

As the fund grows, and when enough shares have been contributed, the fund closes to new shares. Then each investor is given interest in the collective shares based on their portion from the original contributions. The shares in the fund moved to the exchange fund are not immediately subject to capital gains taxation.

Question 158

What is Beta?

Answer 158

Beta is a measure of a stock’s volatility in relation to the market. It measures the exposure of risk a particular stock or sector has in relation to the market. If you want to know the systematic risk of your portfolio, you can calculate its beta.

1. A beta of 0 indicates that the portfolio is uncorrelated with the market.
2. A beta less than 0 indicates that it moves in the opposite direction of the market.
3. A beta between 0 and 1 signifies that it moves in the same direction as the market, with less volatility.
4. A beta of 1 indicates that the portfolio will move in the same direction, have the same volatility and is sensitive to systematic risk.
5. A beta greater than 1 indicates that the portfolio will move in the same direction as the market, with a higher magnitude, and is very sensitive to systematic risk.