Investments Ch 3 Flashcards
RISK AND RETURN
RISK AND RETURN
- Risk - Risk can be defined as the uncertainty of future outcomes.
Involves the uncertainty of future outcomes or the possibility of an
adverse result
- Returns
Individuals forgo consumption for the opportunity of future returns.
Return is the reward for investing
METHODS OF MEASURING RETURNS
METHODS OF MEASURING RETURNS
The two sources of return from an investment are the yield and the
appreciation.
Yield + Capital Gain = Total Investment Return
- Yield - is the amount of cash the investment generates and the amount the investor receives or reinvests during a period. Yield is expressed as a percentage of the amount invested.
- Capital Gain - is the percentage change in the investment’s value from the beginning to the end of the period
EXPECTED AND REQUIRED RATE OF RETURN
EXPECTED AND REQUIRED RATE OF RETURN
Expected
* The level of return an investor thinks an investment will earn in
the future
* The expected return depends on internal and external forces.
Required
* The rate of return an investor must earn on an investment to be
fully compensated for its risk
MEASURES OF RETURNS
MEASURES OF RETURNS
- Holding Period Return * Annualized Return
- Arithmetic Mean Return * Effective Annual Rate of Return
- Geometric Mean Return * Bond Equivalent Yield
- Internal Rate of Return * Weighted Average Return
- Dollar-Weighted * After-tax Return
- Time-Weighted * Real Return
HOLDING PERIOD RETURN (HPR)
HOLDING PERIOD RETURN (HPR)
A measure of return over a specific time and includes:
- Capital gain or loss
- Current income
- HPR is most meaningful if holding period is one year
[Sale Price – Purchase Price +/- cash flows] HPR = --------------------------------------------------------------- Purchase Price
HOLDING PERIOD RETURN:
EXAMPLE
Enrique buys a stock for $60 and receives dividends of $10.
He then sells the stock for $100.
What is his holding period return?
Was this a good return?
HOLDING PERIOD RETURN:
EXAMPLE
Enrique buys a stock for $60 and receives dividends of $10.
He then sells the stock for $100.
What is his holding period return?
$100 - $ 60 + $10
—————————— = 83.33 %
$60
Was this a good return? yes
HOLDING PERIOD RETURN:
EXAMPLE
Enrique buys a stock for $60 and receives dividends of $10.
He then sells the stock for $100.
What is his holding period return?
Was this a good return?
ARITHMETIC MEAN RETURN
Arithmetic return is a simple average return, but it does not account
for compounding.
Year 1 2%
Year 2 4%
Year 3 6%
Year 4 8%
What is the Arithmetic Mean Return?
2 + 4 + 6 + 8
——————— = 5%
4
ARITHMETIC MEAN RETURN: EXAMPLE 1
Consider this example:
Year 1 45%
Year 2 (10%)
Year 3 (25%)
Year 4 30%
What is the Arithmetic Mean Return?
ARITHMETIC MEAN RETURN: EXAMPLE 1
Consider this example:
Year 1 45%
Year 2 (10%)
Year 3 (25%)
Year 4 30%
What is the Arithmetic Mean Return?
45 + (10) + (25) + 30
—————————– = 10%
4
ARITHMETIC MEAN RETURN: EXAMPLE 2
The disadvantage to the Arithmetic Mean is that it doesn’t take
compounding into account.
ARITHMETIC MEAN RETURN: EXAMPLE 2
The disadvantage to the Arithmetic Mean is that it doesn’t take
compounding into account.
Example:
Destiny buys a stock for $100. The stock is worth $200 at
the end of the year. Next year the stock falls back to $100.
What is Destiny’s average return
GEOMETRIC RETURN
GEOMETRIC RETURN
The geometric (mean) is a compounded rate of return.
Better measure of an investor’s effective return over several periods than the arithmetic mean.
The geometric mean of a set of holding period returns for a security is used to calculate: – The time weighted return.
GM = 1 + rଵ 1 + rଶ … (1 + r୬) − 1 x 100
GM = Geometric Mean
n = number of returns
rn = actual return for period n
- The geometric mean formula calculates the average return over time
assuming all earnings remain invested. In other words, the geometric
mean calculates the compound annual return, not the simple average return.
-The greater the volatility of investment returns, the lower the geometric return over time as compared with the arithmetic average return.
-The arithmetic average tends to overstate the average return, especially when both positive and negative returns are experienced.
GEOMETRIC RETURN : EXAMPLE
Year 1 45%
Year 2 (10%)
Year 3 (25%)
Year 4 30%
GEOMETRIC RETURN : EXAMPLE
Year 1 45%
Year 2 (10%)
Year 3 (25%)
Year 4 30%
GM = 1.45 0.90 (0.75)(1.3) − 1 𝑥 100
𝐺M = ర 1.272 − 1 𝑥 100 = 6.2
__________________________________________________
Dalton Instructor formula method:
-You cannot use negative so instead of -10% = .90 and -25% = .75
1 Step 1 solve for FV
1.45 x .90 x .75 x 1.30 = 1.27
- Solve for I
1.2724 FV
-1 PV ( its negative one because a dollar was invested , outflow)
4 N
I = 6.20%
__________________________________
INTERNAL RATE OF RETURN
INTERNAL RATE OF RETURN
The internal rate of return (IRR) is the earnings rate of a series of
cash inflows and outflows over a period of time assuming all earnings
are reinvested. It equates the present value of the future cash flows to the price of the investment.
CF0 = the price of the investment
CFn = the cash flow that occurs at period n
IRR = the rate that forces the price of the investment to be equal to the present value of the cash flows
INTERNAL RATE OF RETURN METHODS
INTERNAL RATE OF RETURN METHODS
________________________________________________________________
Dolla R Weighted - “ from the InvestoR perspective”
- Measures the effect of all cash flows an investor controls
-Combines the result of the timing and dollar volume of investor
trades during a period and the performance of the investment
security
– Used to determine the investor’s combined result of the timing and dollar volume of the transactions during the period, as well as the performance of the investment security. It is also appropriate for gauging the performance of an investment manager with full discretion over an investor’s account.
__________________________________________________________________
T ime Weighted Return - “ from the investmenT perspective”
- Measures the effect of cash flows associated with an investment
- It ignores the dollar volume and timing of investor-driven trades
- It assumes a buy and hold approach
- Mutual funds report their returns using a time weighted return
–More appropriate for assessing the performance of a fund manager or a security.
RR EXAMPLE
Example: Christine purchased 100 shares of Fly Cheap Airlines stock
for $12 per share. One year later the stock paid a dividend of $1 per
share. Christine buys 100 additional shares for $11 per share. At the
end of the second year Christine sells all 200 shares for $20 per share.
What was the time weighted return on Fly Cheap Airline stock?
What was Christine’s dollar weighted return?
RR EXAMPLE
Example: Christine purchased 100 shares of Fly Cheap Airlines stock
for $12 per share. One year later the stock paid a dividend of $1 per
share. Christine buys 100 additional shares for $11 per share. At the
end of the second year Christine sells all 200 shares for $20 per share.
What was the TIME WEIGHTED return on Fly Cheap Airline stock?
0 1 2
I——————-I——————–I-
-12 1 20
-12 CF
1 CF
20 CF
IRR = 33.33%
What was Christine’s DOLLAR WEIGHTED return?
0 1 2
I——————–I——————–I-
-1200 100 4,000
-1,100
-1200 CF
-1000 CF
4000 CF
IRR = 45.60%
ANNUALIZED RETURN
ANNUALIZED RETURN
The annualized return is equivalent to a compound rate of return.
- It assumes that cash flows (i.e., interest, dividends) are reinvested
at the same rate. - If this assumption is not met, then the actual return will be different
than the calculated annualized return. - When investments are held for less than one year, it is useful to
calculate the annualized yield on the investment.
NNUALIZED RETURN: EXAMPLE
Annualized return equation:
Annualized Return = 1 + Rp N − 1
Rp = return for the period being measured
N = number of periods in a year
Assume Jack earned a quarterly return of 3%
.
The annualized rate of return would be:
ANNUALIZED RETURN: EXAMPLE
Annualized return equation:
Annualized Return = 1 + Rp N − 1
Rp = return for the period being measured
N = number of periods in a year
Assume Jack earned a quarterly return of 3%
.
The annualized rate of return would be:
Annualized return = (1.03)4 - 1 = 0.1255 = 12.55%
EFFECTIVE ANNUAL RATE OF RETURN
EFFECTIVE ANNUAL RATE OF RETURN
Takes the impact of compounding into account. When compounding occurs more frequently than annually, the effective annual rate of interest is higher than the nominal rate. The more frequent the compounding, the higher the effective rate
Chelsea invests in a bank CD with a nominal yield of 7% compounded
weekly. Chelsea’s effective annual rate of return is:
i 2 EAR = [ 1 + ------- ] - 1
n
52
.07 [ 1 + -------- ] - 1 = .0725 = 7.25 %
52
BOND EQUIVALENT YIELD (BEY)
BOND EQUIVALENT YIELD (BEY)
BEY determines the yield for a bond sold at a discount based on the
current price and the remaining days until maturity.
Par Value − Price 365
BEY = x , where
Price d
Par value = the face value of the bond, generally $1,000
Price = the price of the bond or the price paid for the bond
d = the number of days until maturity
BOND EQUIVALENT YIELD: EXAMPLE
Example 1: Betty buys a bond with 192 days until maturity for $950.
The BEY is computed as follows:
BOND EQUIVALENT YIELD: BEY
Used to compare yields for bonds with different maturities.
Does NOT work for selling at a premium
Par Value - Price 365 BEY = ------------------------------------------ x -----------
Price d
Par value = the face value of the bond, generally $1,000 Price = the price of the bond in the market or the price paid for the bond 365 = the number of days in a year d = the number of days until maturity
EXAMPLE
Example 1: Betty buys a bond with 192 days until maturity for $950.
The BEY is computed as follows:
$1000 - $950 365 BEY = -------------------------- x -------- = 10 %
$950 192
Example 2: Bobby buys a bond with 289 days until maturity for $931.
The BEY is computed as follows:
$1000 - $931 365 BEY = -------------------------- x -------- = 9.36 %
$931 289
The BEY is often used to compare yields for bonds with different
maturities.
WEIGHTED AVERAGE RETURN
WEIGHTED AVERAGE RETURN
A return that is “weighted” based on the dollar amount of the individual investments.
Rw =
Rw = weighted average return
Ri = return for investment i
Wi = weight for investment i as a percentage of the portfolio
N = number of investments
The overall weighted average return is computed by: 1. summing the market value of the investments, 2. multiplying the percent return of each security by the individual market value to obtain the individual dollar returns, which are then added together, and 3. dividing the total dollar return by the total market value.
Example:
Riley has a portfolio worth $10,000 consisting of three
stocks. The expected return for each stock is given, along with its
proportionate value of the portfolio. What is the expected return for the portfolio?
Stock Expected Return Value
Apple 20% $3,000
Google 25% $3,000
Amazon 50% $4,000
WEIGHTED AVERAGE RETURN: EXAMPLE
Stock Expected Return % of Portfolio Weighted Return
__________________________________________________________________
Apple 20% 30% 6.0
Google 25% 30% 7.5
Amazon 50% 40% 20
WEIGHTED AVERAGE RETURN: EXAMPLE
Stock Expected Return % of Portfolio Weighted Return
__________________________________________________________________
Apple 20% 30% 6.0
Google 25% 30% 7.5
Amazon 50% 40% 20
= 33.5%
(20%)(0.30) + (25%)(0.30) + (50%)(0.40) = 33.5%
AFTER-TAX RETURNS & CAPITAL GAINS
AFTER-TAX RETURNS & CAPITAL GAINS
After-Tax Return = Taxable Return x (1 – Marginal Tax Rate)
- Realized taxable return = the return from the investment without
considering income tax
investors in high marginal income tax brackets should evaluate investments based on their after-tax returns to determine whether any of the investment options have some sort of tax advantage or penalty
- Marginal income tax rate = the tax rate percentage applied to
incremental taxable income
EXAMPLE:
Hank compares a corporate bond with a municipal bond. The corporate offers a yield to maturity of 5% while the muni has a yield of just 4%.
At first glance, it appears the corporate offers a superior investment. Hank, however, pays taxes at a marginal rate of 30% and will receive tax benefits from the muni bond, but not from the corporate. In fact, the after-tax return of the corporate will be only 3.5% or [5% x (1 - 30%)], making it less attractive than the muni.
EXAMPLE
The equation can be rearranged or solved for the tax rate that equates two bonds subject to different tax treatment. Consider the following example.
Jesse is considering a corporate bond yielding 8.0% and a municipal bond yielding 5.6%. The tax rate at which Jesse would be indifferent between the two bonds is 30%, as follows:
8.0% x (1 - Tax rate) = 5.6%
1 - Tax rate = 70%
Tax rate = 30%
-If Jesse’s marginal rate is less than 30%, then he would be better off from an after-tax perspective with the corporate bond.
i.e. 8.0% x ( 1 - .25 ) = 6.00 ( so if in 25 % tax bracket, then the corporate is better.
-If his tax rate is in excess of 30%, then he would be better off with the municipal bond.
REAL RETURN
Example: Benji has a retirement fund that is expected to earn 9%
annually, but inflation is 3%. Benji’s real annual return is =
REAL RETURN
Inflation erodes purchasing power. When attempting to estimate the
future purchasing power (investment returns net of inflation), the
inflation-adjusted, or real rate of return is appropriate
1 + Rn Real Rate of Return = ( ----------- - 1 ) x 100
1 + i
Rn = nominal rate or Return ,
i = inflation
Example:
Benji has a retirement fund that is expected to earn 9%
annually, but inflation is 3%. Benji’s real annual return is =
1.09% [ ( -------------- -1 ) x 100 ] = 5.83%
1.03 %
RISK
RISK
- Risk involves the uncertainty associated with returns.
- The chance that the actual return from an investment may differ from what is expected
- The more risk, the higher the return required.
- Risk in the context of Investments, has two components:
—Systematic or Market Driven
—Unsystematic or Unique (specific to the security)
TOTAL RISK
TOTAL RISK
- Total Risk = Systematic + Unsystematic Risk
- Total risk is measured by standard deviation.
- Systematic risk is measured by beta.
SYSTEMATIC RISK
SYSTEMATIC RISK “prime “
- Purchasing Power
- Reinvestment Rate
- Interest Rate
- Market Risk
- Exchange Rate
- Systematic (Non-Diversifiable Risk)
- Systematic risks are those risks that are inherent in the “system.”
- These risks are non-diversifiable, regardless of how many securities and industries are combined in a portfolio
—–No amount of diversification can reduce or eliminate systematic risk.
UNSYSTEMATIC RISK
UNSYSTEMATIC RISK
Unsystematic risk can be diversified away by combining multiple asset classes and industries in a portfolio.
Unsystematic (Diversifiable Risk) Risk includes:
* Business
* Country
* Credit or Default
* Financial
* Government / Regulation
* Others include: Call Risk, Investment Manager, Event Risk, Liquidity
and Marketability Risk
STANDARD DEVIATION
STANDARD DEVIATION
- Measure of TOTAL RISK = Systematic + Unsystematic Risk
- The greater the standard deviation, the greater the risk
- Measure of total return variability
- Measures variation of returns around an average
The variance of a distribution is its standard deviation squared.
Measures variability of returns in relation to the mean return.
A larger standard deviation implies greater uncertainty of outcomes.
With a normal distribution,_________________________________________
approximately 68% of the outcomes fall within ± 1 standard deviation from the mean,
approximately 95% of the outcomes fall within ± 2 standard deviations from the mean,
and approximately 99% of the outcomes fall within ± 3 standard deviations from the mean.
POPULATION STANDARD DEVIATION
POPULATION STANDARD DEVIATION
Measure the risk for a population
The variation of the # of returns within the entire population
𝑟௧ = past returns
𝑟̅ = arithmetic mean of past returns
n = number of returns used
𝜎 = population standard deviation
SAMPLE STANDARD DEVIATION
SAMPLE STANDARD DEVIATION
The calculation will be a little larger since its from a sample within the population.
𝑟௧ = past returns
𝑟̅ = arithmetic mean of past returns
n = number of returns used
𝜎 = sample standard deviation
CALCULATE STANDARD DEVIATION
Calculate the standard deviation of the following annual returns:
Year 1 5%
Year 2 9%
Year 3 1%
Year 4 (2%)
Year 5 7%
CALCULATE STANDARD DEVIATION
example
Calculate the standard deviation of the following annual returns:
Year 1 5%
Year 2 9%
Year 3 1%
Year 4 (2%)
Year 5 7%
5 +
9
1
-2
7
orange shift Sx.Sy = 4.47%
POPULATION STANDARD DEVIATION: EXAMPLE
POPULATION STANDARD DEVIATION: EXAMPLE
SAMPLE STANDARD DEVIATION: EXAMPLE
SAMPLE STANDARD DEVIATION: EXAMPLE
PROBABILITY OF RETURNS ASSUMING A
NORMAL DISTRIBUTION
PROBABILITY OF RETURNS ASSUMING A
NORMAL DISTRIBUTION
The following exhibit helps to explain the relationship between standard deviation and probabilities of outcomes
The curve in Exhibit 3.5 shows the bell-shaped curve of a normal distribution.
The vertical axis represents the probability of observing an outcome and the horizontal axis represents the possible outcomes.
The curve peaks at the mean of the distribution, as the mean is the most likely outcome to be observed.
Observing values further and further away from the mean becomes less and less likely, hence the curve slopes down towards the tails. The likelihood of seeing observations far out in the tails becomes extremely low, but never quite hits zero
DISTRIBUTION OF RETURNS
- Normal Distribution
- Classic Bell Curve Distribution of Data
- Distributions that are NOT normal. May be caused by:
- Skewness
- Kurtosis
DISTRIBUTION OF RETURNS
- Normal Distribution
- Classic Bell Curve Distribution of Data
- Distributions that are NOT normal. May be caused by:
- Skewness
- Kurtosis
DISTRIBUTION OF RETURNS: SKEWNESS
DISTRIBUTION OF RETURNS: SKEWNESS
Skewness: Measures the lack of symmetry in a Bell Curve
- Skewness for a normal curve is zero.
- Data skewed to the left has negative skewness.
- Data skewed to the right has positive skewness.
- Example: T-Bill returns are positively skewed since returns cannot
be negative
KURTOSIS
DISTRIBUTION OF RETURNS: KURTOSIS
Degree to which Bell Curves are peaked or flat at the top.
High Kurtosis data is peaked at the mean;
low Kurtosis data is rounded at the mean.
The Kurtosis for normal data is 3.
BETA: A MEASURE OF SYSTEMATIC RISK
BETA: A MEASURE OF “SYSTEMATIC RISK”
Beta is used to measure the volatility of a portfolio as compared to the market. Beta measures systematic risk only
Beta is an indication of a security’s volatility relative to the market. The market is defined as having a beta of 1.0.
Beta can be used as a measure of risk for portfolios that are sufficiently diversified to eliminate unsystematic risk.
- ABC Stock Beta = 1.5
- ABC returns should be 50% more volatile than market returns. If
the market increases by 10%, then ABC returns are expected to
increase by 1.5 x 10% = 15%. - What if the market decreases by 5%?
- XYZ Stock Beta = 0.7
- XYZ returns should be 30% less volatile than market returns. If
the market increases by 10%, then XYZ returns are expected to
increase by 0.7 x 10% = 7%.
BETA: THE FORMULA
BETA: THE FORMULA
(Std Dev of investment) ( Correlation between asset & market) BETA = -------------------------------------------------------------------------------------
Std Dev of Market
Cov im (P im ) ( σ i ) βi = \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ = \_\_\_\_\_\_\_\_\_\_\_\_\_\_
2 σ m
σ m
βi = beta of asset i
Cov im = covariance between asset i and the market
Rim = correlation between asset i and the market
σ i = standard deviation of asset i
σ m = standard deviation of the market
P im = Correlation coefficient between the individual security and the market
DERIVING BETA
DERIVING BETA
- Relationship between a security’s return and the market return
- Derived by plotting a security’s return on the y-axis and market’s return on the x-axis
- Beta is simply Rise ÷ Run or the slope of the line that best represents the security’s returns and market returns.
- Beta can be positive or negative, but most are positive
CORRELATION AND DIVERSIFICATION
CORRELATION AND DIVERSIFICATION
Correlation is a statistical measure of the relationship, if any, between two variables.
Ranges from +1.0 (perfectly positively correlated) to -1.0 (perfectly negatively correlated).
- The coefficient of determination, which is represented as r2 or R2, measures the percentage of the change in the portfolio that is explained by the change in the market.
- The R2 value represents the amount of systematic risk in the portfolio. The amount of unsystematic risk is equal to 1 – R2.
- Correlation can be positive, negative, or zero.
- Correlation provides insight to the strength and direction two assets
move relative to each other. - Correlation, also called the correlation coefficient, is represented
with the symbol or R
CORRELATION
CORRELATION
TOTAL RISK & DIVERSIFICATION
TOTAL RISK & DIVERSIFICATION
R-SQUARED
R-SQUARED
Measures the degree of a portfolio’s diversification
R2 = Coefficient of determination ranges from 0 to +1.
- R-squared (the coefficient of determination) is represented by R2.
- R-squared indicates the reliability of the model or the reliability of
Beta. - R-squared indicates the percent of return that is due to the market
(when the portfolio is being compared to an index). - R-squared is calculated by squaring the correlation coefficient.
- Correlation (R) = 0.8
- R2 = 0.64 or 64%
- R-squared is a measure of how well diversified your portfolio is.
- An S&P 500 Index Fund will have an r-squared = 100%
- A Sector Mutual Fund will have an r-squared between 40-50%
OTHER MEASURES OF TOTAL RISK
Semi-Variance
Coefficient of variation (CV)
OTHER MEASURES OF TOTAL RISK
Semi-Variance______________________________________________
–Similar to standard deviation; it measures the variation in returns that were below the average return and excludes the returns that exceeded the average return.
Coefficient of variation (CV)__________________________________
Standard Deviation CV = ------------------------------
Avg Return
–Measures risk relative to return. Useful when comparing the risk of assets with differing average or expected returns.
– The higher the CV, the greater the risk per unit of return.
– Investor prefers the asset with the lower coefficient of variation
because it has less risk for each unit of return (which also equates
into more return per unit of risk)
–The coefficient of variation measures the amount of risk per unit of return.
COMPARING INVESTMENT ALTERNATIVES
COMPARING INVESTMENT ALTERNATIVES
- When comparing two investment alternatives:
- The one with the higher standard deviation has more risk.
- If average returns are equal, the investment with the larger
standard deviation has greater risk per unit of return. - If their average returns are not equal, then calculate the
coefficient of variation to determine which has the greater risk
per unit of return. - Lower is better (less risk per unit of return)
MEASURING RISK: EXAMPLE
Which investment appears riskier?
Which provides the lowest risk per unit of return?
Average Return 12 20
Standard Deviation 9 10
CV ? ?
MEASURING RISK: EXAMPLE
Which investment appears riskier?
Which provides the lowest risk per unit of return?
Average Return 12 20
Standard Deviation 9 10
CV ? ?
Standard Deviation CV = ----------------------------------------------
Average or Expected Return
The real return (inflation-adjusted return) adjusts the nominal return to reflect the impact of inflation.
Real rates of return are used in retirement funding, education funding and other calculations that require the incorporation of two different types of rates, such as an earnings rate and an inflation rate
Short-term T-bills
Short-term T-bills are generally regarded as the closest available choice to a risk-free investment because they are backed by the full faith and credit of the U.S. government.
Investors in growth stocks paying no dividends, and investors owning zero-coupon bonds need not be concerned with reinvestment rate risk since they do not receive any periodic cash flows from those investments.
Marketability
Marketability
investor’s ability to easily find a market to sell their investment.
Liquidity
Liquidity
Ability to sell an investment quickly at a competitive price without any loss of principal or any price concessions.
Value at Risk is a risk management tool that ?
Value at Risk is a risk management tool that
quantifies (in terms of a percentage loss or in terms of dollars) the level of risk during a specific time period.
Exchange Rate Risk
Assume that an American’s investment in the stock of a French company yielded a nominal rate of return of 18% in the past 12 months. Assume also that the Euro was worth $0.20 at the start of the period and $0.25 at the end of the period.
In this case, the true rate of return for the investor was:
a. -5.6%. b. 11.3%. c. 22.5%. d. 47.5%
Exchange Rate Risk
-The uncertainty of returns in foreign investments due to changes in the value of a foreign currency relative to the valuation of the investor’s domestic currency is referred to as exchange rate risk.
EXAMPLE :
The euro increased in value during the holding period.
If the investor started with $100 and the euro was
0.20 per USD, then the investor could exchange their $100 for 500 Euros.
- What is the conversion from USD to EURO
$ 100 USD
—————- = 500 EUROS
.20 EURO - The investment then grew by a nominal rate of :
18% (500 EU x 1.18 = 590 EU). - To bring the Euros back to dollars when the euro is now
worth 0.25 per USD (590 x 0.25 = $147.50). - Therefore, the investor’s return was more than the nominal
18%. Specifically, it was:
[1.18 x (0.25÷0.20)] - 1 = 47.5%
coefficient of variation (CV).
Coefficient of variation (CV).
measures the amount of risk per unit of return
Determines which investment is riskier when investments have different avg returns
The higher the CV the more risky an involvement and the less likely an investor is to experience the avg rate of return.
Standard Deviation cv = ------------------------------------
Average Return
the 4 C’s
Coefficient of Variation: ________________________________
Standard deviation divided by expected return (total risk per unit of return).
Standard deviation
—————————- = Coefficient of Variation:
expected return
Correlation Coefficient: ____________________________________
Ranges from –1.0 to + 1.0. Maximum risk reduction occurs at perfect negative correlation (–1.0). No risk reduction occurs at perfect positive correlation (+1.0).
Covariance:
A measure of how much two assets move together.
Coefficient of Determination:
Known as R2 this statistic provides the percentage variation in portfolio returns that is explained by the variation in the benchmark returns.
this is all rote memorization really.
I always remember that left skewed is where the tail goes (tail points/skews out to the left), hopefully that little trick helps. Although you should know all the material, there’s not a high likelihood of seeing this is on the exam
Correlation Coefficient:
COV ab P ab = ----------------------------
(σA ) ( σB )
p ab = Correlation coefficient of assets A and B
σA = Standard deviation of asset A
σB = Standard deviation of asset B
COV ab = Covariance of Assets A and B
-Correlation and the Covariance measure movement of one security relative to that of another.
-Covariance and correlation coefficient are both “relative “ measures.
Correlation ranges from =1 to -1 provide the investor with insight as to the strength and direction 2 assets move relative to each other.
- Correlation of +1 = the 2 assets are perfectly positivity correlated
- Correlation of 0 = the assets are completely uncorrelated.
- Correlation of -1 = the assets are negatively correlated.
- Diversification benefits ( risk is reduced) BEGIN anytime correlation in less than +1
COVARIANCE
COVARIANCE
Measure of how much 2 assets move together.
Measure of “Relative Risk “
How price movements between 2 companies are related to one another.
Combines the volatility of one asset’s returns with the tendency of those returns to move up or down at the same time that another asset’s returns move up or down.
CovAB = ( σA ) ( σB) ( RAB)
CovAB = Covariance between assets A and B
σA = Standard deviation of asset A
σB = Standard deviation of asset B
RAB = Correlation Coefficient between assets A and B
Sylvia has a two assets in her portfolio, asset A and asset B. Asset A has a standard deviation of 40% and asset B has a standard deviation of 20%. 50% of her portfolio is invested in asset A and 50% is invested in asset B. The correlation for asset A and asset B is .90. What is the standard deviation of her portfolio?
Greater than 30%. Less than 30%. Equal to 30%. Not enough information to determine.
Solution: The correct answer is B.
It’s not necessary to use the standard deviation of a two asset portfolio formula to answer this question.
Since there’s a 50/50 weighting for each asset, simply take a simple average of the standard deviations (.40 + .20) ÷ 2 = .30. Since the correlation is less than 1, the standard deviation for the portfolio will be less than the simple average. If correlation was equal to 1, then the standard deviation would be equal to 30%.
Diversification - Comparing the variability of a portfolio’s return to the market indicates
Weighted average return - The Combined Return of a portfolio is the:
Adjusted for correlation -The Combined Standard Deviation of a portfolio is the weighted average
Diversification - Comparing the variability of a portfolio’s return to the market indicates
Weighted average return - The Combined Return of a portfolio is the:
Adjusted for correlation -The Combined Standard Deviation of a portfolio is the weighted average
Standard Deviation -
Beta
R-squared to the market
Standard Deviation - Measures total risk
The standard deviation is a measure of a distribution’s dispersion around its mean.
Beta - Measures systematic risk
R-squared to the market - Measures the degree of a portfolio’s diversification
The type of risk which measures the extent to which a firm uses debt securities and other forms of debt in its capital structure to finance is known as:
Business risk Systematic risk Default risk Financial risk
Solution: The correct answer is D.
Financial risk has to do with the amount of leveraging or use of borrowed funds a firm utilizes to structure its investment and finance its assets
A bond fund had the following yearly returns:
Year 1 at 14%
Year 2 at 7%
Year 3 at -3%
Year 4 at 18%
Year 5 at 9%
What is the standard deviation of the returns?
6.04 7.13 7.97 8.43
HP 10BII
.14 ∑+
.07 ∑+
.03 +/- ∑+
18 ∑+ .
.09 ∑+
Orange shift, SxSy (8 key)
.07969 = 7.969%
Michael has an investment with the following annual returns for four years:
Year 1: 12%
Year 2: -5%
Year 3: 8%
Year 4: 18%
What is the arithmetic mean (AM) and what is the geometric mean (GM)?
AM = 8.25%, GM = 7.91% AM = 8.25%, GM = 10.64% AM = 10.75%, GM = 7.91% AM = 10.75%, GM = 10.64%
Solution: The correct answer is A.
AM = (.12 -.05 + .08 + .18) / 4 = .0825 = 8.25%
GM = (1.12 × .95 × 1.08 × 1.18) ^ (1/4) - 1 × 100
GM = (1.356) ^ (1/4) - 1 × 100
GM = 7.91%
What is the weighted average beta of the following portfolio? Stock L has a beta of 1.45 and constitutes 10% of the portfolio, stock M has a value of $125,000 with a beta of .93, while stock N makes up 40% of the portfolio with a beta of .65, and stock O, with a 2.2 beta has a dollar value of $175,000.
1.24 1.31 1.54 1.76
Be certain to avoid rounding errors in arriving at the correct solution. For weighted average beta, use only the two places to the right of the decimal.
Stock L = 10%;
Stock M=$125,000;
Stock N=40%;
Stock O=$175,000;
L+N=50%; therefore M+O=50% or $300,000.
Thus the total portfolio value is $600,000.
______________________________________________________________
Stock L = $60,000/$600,000 = .10 × 1.45 = .15;
Stock M = $125,000/$600,000 = .2083 × 0.93 = .19;
Stock N = $240,000/600,000 = .40 × 0.65 = .26;
Stock O = $175,000/$600,000 = .2917 × 2.2 = .64.
_______________________________________________________________
Adding the results
(.15+.19+.26+.64=1.24)
will result in the weighted average beta of 1.24.
Bob Conrad’s investment portfolio consists of several types of stocks, bonds, and money market instruments. The portfolio has an overall standard deviation of 12%, a beta of 1.06, and a total return for the year of 11%. Bob is considering adding one of two alternative investments to his portfolio. Stock A has a standard deviation of 13%, a beta of .87, and a correlation coefficient with the portfolio of .6. Stock B has a standard deviation of 11%, a beta of .97, and a correlation coefficient of .95.
Which stock should Bob consider adding to his portfolio, and why?
Stock A, because it has a lower correlation coefficient. Stock A, because it has a lower beta than that of the portfolio. Stock B, because it has a lower standard deviation than that of the portfolio. Stock B, because it has a higher correlation coefficient.
Solution: The correct answer is A.
In the process of adding new investments to a portfolio,
The lowest correlation coefficient makes the best addition. Closest to negative one (-1) is always best.
The type of risk which CANNOT be eliminated through diversification is:
Unsystematic risk Company specific risk Systematic risk Business risk
Systematic risk
Waste Management increased the salvage value and extended the useful life of their garbage trucks. This action resulted in decreasing and deferring expenses. What type of risk does this describe?
nterest rate risk.
Market risk.
Business risk.
Accounting risk.
Accounting risk.
Rationale
Accounting risk is the risk that financial statements do not accurately reflect the financial condition of a business due to fraud or error.
Portfolio C has a standard deviation of 20% and a correlation with the market of 0.9. If the standard deviation of the market is 18%, what is the beta for C?
1.00.
Rationale
Beta equals the standard deviation of the portfolio times the correlation divided by the standard deviation of the market: (0.2 x 0.9)÷ 0.18 = 1.00
(Std Dev of investment) ( Correlation between asset & market) BETA = -------------------------------------------------------------------------------------
Std Dev of Market
The “doctor” describes himself as a “swinging for the fences” type of investor. He invests in 1 stock ABC that has a beta of 0.75 and concludes that he is only taking 3/4 of the risk of the market. Is he right?
No, beta only measures systematic risk.
Rationale
Beta only measures systematic risk. Since the doctor has only one stock, he has a lot of unsystematic risk as well. Therefore, he is incorrect.
Consider a firm with assets of $200 and equity of $200.
This firm issues $50 in debt with a 10% annual interest rate to repurchase $25 in equity and to invest $25 into the business.
The first year after issuing the debt, the firm has $18 in operating income.
Compute the firm’s return on equity, ignoring tax.
7.4%.
Interest expense = $50 × 0.10 = $5
Equity is $200 – $25 after the repurchase = $175
earnings per share
( $18 Op Inc. – $5 interest )
---------------------------------------------- = 0.07429 ROE
$175
shareholders equity
A commercial bank owns a portfolio of fixed income securities with a market value of $810 million. The bank is concerned about a spike in inflation during the coming month, citing a potential energy shortage. A surge in oil and natural gas price would place significant downward pressure on the value of the portfolio. The risk management measure most likely to help the bank is:
Value at risk.
Rationale
While beta and standard deviation are excellent risk management measures, they are designed to identify long-term risks and variability. They reveal very little about short-term risk. Value at risk, however, was developed as a result of the 1987 crash to help banks manage the potential losses during market downturns, especially over shorter terms.
Uncle Robbie, who lives in Kenner, Louisiana, bought a Treasury bond on the secondary market that has 10 years until maturity and a 2% coupon payment, paid semi-annually. Which of the following risks is he subject to?
Reinvestment rate risk
Amelia bought Acme, Inc. for $40 per share two years ago. Today, Acme is trading at $72 per share.
What is the annualized return for Amelia?
80.00%.
40.00%.
34.16%.
28.75%.
34.16%.
72 - 40
1. holding period return = ———————— .80 = 80%
40
Annualized return equation:
n Annualized Return = ( 1 + Rp ) − 1
Rp = return for the period being measured
N = number of periods in a year
- Annualized return = (1.8) ^ 1/2 - 1 = 34.16%
OR
2 N
-40 PV
72 FV
0 PMT
I = 34.16%
Which of the following correlations represents the weakest relationship between two variables?
Correlation = -1.00.
Correlation = -0.40.
Correlation = +0.18.
Correlation = +0.88.
Correlation = +0.18.
The strongest relationship exists at +1 and -1. The weakest relationship is at zero.
Thus, the weakest relationship is 0.18 in this list.
Which of the following statements concerning risk and return is not correct?
inflation risk, or purchasing power risk, is the variability in securities returns caused by a decline in the purchasing power of the invested dollars.
Rationale
Option a is incorrect as inflation risk is not associated with the variability in securities returns. Rather, it is the decline in purchasing power of the amounts invested.
Bubba, who lives in Scotland, invested £1 million in IBM, a U.S. company, trading at a market value of $85 per share.
The conversion rate for pounds to dollars was £1 to $1.65 at the time of the investment.
Assume that after two years, the stock doubles in price and he sells the stock when the conversion rate for pounds to dollars is £1 to $2.00.
How much is his gain in pounds?
Initial investment of £1 million at an exchange rate of $1.65 will buy $1.65 million.
If the market price of the share doubles, so will the value of the dollar investment, hence Bubba will have $3.3 million ($1.65 x 2) at the end of the two-year period.
The exchange rate on the date of sale has moved to $2.00 per £1, so the sales proceeds will be
£1.65 million ($3.3 million divided by 2). Bubba has therefore turned his initial £1 million into £1.65 million and gained £0.65 million.
_____________________________________________________________________
The percentage gain can also be calculated using the nominal yield (100%) and the currency movement. The foreign currency (USD) weakened against GBP, it takes $2 to buy £1 at the date of sale but only $1.65 initially. This means at the date of sale $1 buys £0.50 (1/$2) and initially $1 bought £0.606 (1/$1.65). USD has therefore weakened by 17.50% [(0.5/0.606) – 1].
Bubba’s gain is therefore
[(1 + 100%) x (1 – 17.50%)] – 1 = (2 x 0.825) – 1 = 65%. R2
A portfolio has three stocks as follows:
Portfolio Percentage Beta
Stock 1 50% 2.0
Stock 2 20% 0.7
Stock 3 30% 0.6
What is the weighted beta of the portfolio?
1.32.
Rationale
(0.50 x 2) + (0.20 x 0.7) + (0.30 x 0.6) = 1.32
Assume that an American’s investment in the stock of a French company yielded a nominal rate of return of 18% in the past 12 months. Assume also that the Euro was worth $0.20 at the start of the period and $0.25 at the end of the period. In this case, the true rate of return for the investor was:
47.5%.
Rationale
The euro increased in value during the holding period. If the investor started with $100 and the euro was 0.20 per USD, then the investor could exchange his $100 for 500 Euros.
The investment then grew by a nominal rate of 18% (500 EU x 1.18 = 590 EU). To bring the Euros back to dollars when the euro is now worth 0.25 per USD (590 x 0.25 = $147.50).
Therefore, the investor’s return was more than the nominal 18%. Specifically, it was: [1.18 x (0.25/0.20)] - 1 = 47.5%
end of period of currency total return = ( 1 + NR ) x ----------------------------------------- - 1
begin of period of currency
.25 ( 1+.18 ) x ------------ - 1 = 47.50%
.20
Which of the following correlations represents the strongest relationship between two variables?
Correlation = -1.00
Rationale
The strongest relationship exists at +1 and -1. The weakest relationship is at zero.
Pablo has $1 million saved for retirement. He expects to retire in 15 years. His retirement fund is expected to earn a nominal rate of 9%, and the inflation rate is estimated at 3%. How much money (in millions) should Pablo have when he retires, in real dollars?
2.3m.
Real return = (1.09/1.03)-1 = 5.8252%
FV = $1m x (1.058252)^15 = $2.34m
Alternatively, on a financial calculator enter:
PV = ($1,000,000)
N = 15
i= 5.8252
PMT = 0
Solve for FV = $2,337,957
The “doctor” describes himself as a “swinging for the fences” type of investor. He invests in 1 stock ABC that has a beta of 0.75 and concludes that he is only taking 3/4 of the risk of the market. Is he right?
No, beta only measures systematic risk.
Rationale
Beta only measures systematic risk. Since the doctor has only one stock, he has a lot of unsystematic risk as well. Therefore, he is incorrect.
- Calculate a Holding Period Return
- HPR =
- Lisa bought a stock for $40 and sold it 9 months later for $43.
While she owned the stock she received $.30 in dividends each
quarter. What is Lisa’s holding period return?
- Calculate a Holding Period Return TEST
Measure of return over a specific time and includes:
- Capital gain or loss and Current income
- HPR is most meaningful if holding period is one year
[Sale Price – Purchase Price +/- cash flows] HPR = --------------------------------------------------------------- Purchase Price - Lisa bought a stock for $40 and sold it 9 months later for $43.
While she owned the stock she received $.30 in dividends each
quarter. What is Lisa’s holding period return?
3 qtrs of div is .30 x 3 = .90
43 - 40 + .90
——————– = .0975 = 9.75 %
40
- What does it mean to be risk averse?
- Calculate the standard deviation given a set of returns:
4%, 19%, 11%, 10%
- What does it mean to be risk averse? TEST
Tendency to avoid risk and have a low risk tolerance. Risk-averse investors prioritize the safety of principal over the possibility of a higher return on their money. They prefer liquid investments. - Calculate the standard deviation given a set of returns:
4%, 19%, 11%, 10%
= 6.16 %
Σ+ Σ+
g . Orange shift 8 (Sx,Sy)
- Coefficient of Variation – measure of relative dispersion
- Know the formula
- Know when CV is useful and why
− Comparing assets with different risks and returns - Describe what CV is telling you
TEST
Coefficient of Variation – measure of relative dispersion
(“Dispersion -the act of spreading something ) “
Measures the amount of risk per unit of return
Determines which investment is riskier when investments have different avg returns
- Know when CV is useful and why___________
− Comparing assets with different risks and returns
Higher the CV the more risky an involvement and the less likely an investor is to experience the avg rate of return.
Useful when comparing the risk
-Describe what CV is telling you__________________
* The higher the CV, the greater the risk per unit of return.
* An investor prefers the asset with the lower coefficient of variation because it has less risk for each unit of return (which also equates into more return per unit of risk).
- Know the formula
Standard Deviation
CV = ————————————
Average Return
TEST
* Calculate the weighted average portfolio return.
EXAMPLE:
* Three securities, X, Y, and Z make up the portfolio. The
shares of ‘X’ in the portfolio have a market value of
$10,000 and during the period returned 15%. ‘Y’ has a
market value of $15,000 and returned 12%. ‘Z’ has a
market value of $25,000 and returned 10% over the period.
%of port return weighted return x $10,000 20% 15% = 3%
y $15,000 30% 12 % = 3.60%
z $25,000 50% 10% = 5.00%
TOTAL $50,000
OR
return x $10,000 x 15% = $1,500
y $15,000 x 12% = $1,800
z $25,000 x 10% = $2,500
TOTAL $50,000 $5,800
$5,800
———– = .0116 = 11.60%
$50,000
Systematic Risks are PRIME TEST
* Purchasing Power Risk
* Reinvestment Rate Risk
* Interest Rate Risk
* Market Risk
* Exchange Rate Risk
Unsystematic Risks are ABCDEFG
* Accounting Risk
* Business Risk
* Country Risk
* Default Risk
* Executive Risk
* Financial Risk
* Government/Regulation Risk
Stock index funds and exchange traded funds are subject to which
of the following risks?
A. Financial Risk
B. Interest Rate Risk
C. Systematic Risk
D. Unsystematic Risk
E. Diversifiable Ris
TEST ?????
Stock index funds and exchange traded funds are subject to which
of the following risks?
A. Financial Risk
B. Interest Rate Risk
C. Systematic Risk ««< correct answer ??
D. Unsystematic Risk
E. Diversifiable Risk
Correlation TEST
Positively correlated +1
* Uncorrelated 0
* Negatively correlated -1
Systematic vs. Unsystematic Risk
* Measures of each
* Relevant risk when designing a portfolio?
- Beta TEST
- Calculate
- Definition
- Represents
- Which is more risky? Portfolio A has a Beta = .35
Portfolio B has a Beta = .50 - Beta is a measure of systematic risk or market risk, whereas standard deviation is a measure of total risk.
- Beta is the slope of the regression line (asset returns regressed against benchmark returns)
- Beta is an appropriate measure of risk for a well diversified portfolio
BETA TEST
* The beta coefficient is a measure of an individual security’s
volatility relative to that of the market.
- It measures systematic risk dependent on the volatility of the
security relative to that of the market.- The beta of the market is 1
- It should also be noted that the greater the beta coefficient of
a given security, the greater the systematic risk associated
with that particular security
Coefficient of Determination or R-Squared TEST
- Measure of how much return is due to the market.
- Calculate r2 by squaring the correlation coefficient. For
example:
− If mutual fund XYZ has a correlation coefficient of .80,
then its r2 is .64, which means 64% of fund XYZ’s return is
due to the market.
− r2 also provides insight into how well diversified a
portfolio is. The higher the r2, the higher percentage of
return from the market (systematic risk), the less from
unsystematic risk.
− r2 also indicates if Beta is an appropriate measure of risk
Exam Tip: In a perfectly diversified portfolio,
the only relevant risk is systematic risk.
TEST
Mutual fund XYZ has a 5 year return of 12%, with a standard
deviation of 15%. Fund XYZ has a Beta of 1.4, with a correlation of .90
to the S&P 500. What percent of the return from fund XYZ is due to
the S&P 500?
A. 90%
B. 81% «< correct
C. 19%
D. 10%
Answer”:
R2 is the answer- Squared provided the % of return that is due to the market.
R2 = security correlation squared = .90 squared= .81 = 81%
Which of the following indexes is an appropriate benchmark for Joe
to measure his portfolio against?
A. Index 1
B. Index 2
C. Index 3
D. Index 1 and 2
E. Index 1 and 3
TEST
Which of the following indexes is an appropriate benchmark for Joe
to measure his portfolio against?
A. Index 1
B. Index 2
C. Index 3 «_space;«< Highest R2 best captures the portfolio ???
D. Index 1 and 2
E. Index 1 and 3
When considering a diversified portfolio, which of the following is an
appropriate measure of risk?
A. Standard deviation
B. Beta
C. Covariance
D. Coefficient of determination
E. Correlation coefficient
TEST
When considering a diversified portfolio, which of the following is an
appropriate measure of risk?
A. Standard deviation
B. Beta ««_space;answer
C. Covariance
D. Coefficient of determination
E. Correlation coefficient
Portfolio B has a standard deviation of 12% and a correlation with the market of 0.85. If the standard deviation of the market is 15%, what is the beta for B?
Portfolio B has a standard deviation of 12% and a correlation with the market of 0.85. If the standard deviation of the market is 15%, what is the beta for B?
Beta equals the standard deviation of the portfolio times the correlation divided by the standard deviation of the market:
0.12 x 0.85
——————- = .68
0.15
Which of the following statements concerning beta are correct?
Beta measures total risk. The higher the beta, the higher the expected return. A beta can be positive, negative, or equal to zero. A beta of .35 indicates a lower rate of risk than a beta of negative 0.50. II and III only I and IV only
C II, III and IV only
I, II, III and IV
Solution: The correct answer is C.
The higher the beta, the higher the expected return.
A beta can be positive, negative, or equal to zero.
A beta of .35 indicates a lower rate of risk than a beta of negative 0.50.
