Portfolio Theory

Question 1

Standard Deviation

Answer 1

Measure of risk and variability of returns

• huger the standard deviation, higher the riskiness of the investment.
• can be used to determine total risk of an UNDIVERSIFIED portfolio

For CFP exam need to be able to:
1.use standard deviation to determine the probability of returns

2. Calculate the standard deviation

Question 2

Standard deviation to calculate probability of returns

Answer 2

Graph illustrates a normal distribution with probabilities between -3,-2,-1 & 1,2,3

Question 3

Standard deviation - example

Question 4

Calculating Standard Deviation

Answer 4

CFP exam may ask “which of the following assets is more risky?”

They are really asking you to calculate the standard deviation and select the asset with the highest standard deviation

Question 5

Calculating total expected return

Answer 5

-calculation is sum of all expected returns returns multiplied by their respective probabilities

Question 6

Coefficient Of Variation

Answer 6

• useful in determining which investment has more relative risk when investments have different average returns.
• higher coefficient of variation the more risky an investment per unit of return.

CV = standard deviation/average return

Question 7

Lognormal Distribution

Answer 7

-appropriate if an investor is considering a dollar amount or portfolio value at a point in time.

Question 8

Kurtosis

Answer 8

-variations of returns

Leoptokurtic - high peak and fat tails (higher chance of extreme events)

Platykurtic - low peak and thin tails (lower chance of extreme events)

Question 9

Mean Variance Optimization

Answer 9

• process of adding risky securities to a portfolio but keeping the expected return the same.
• balance of combining asset classes that provide lowest variance as measured by standard deviation

Question 10

Monte Carlo simulation

Answer 10

-spreadsheet simulation that gives probabilistic distribution of events occurring..

Monroe Carlo simulation adjusts assumptions and returns the probability of an event occurring depending on the assumption.

Question 11

Co-Variance

Answer 11

• is the measure of two securities combined and their interactive risk. How price movements between the two are related two each other.
• measure of relative risk
• formula provided on the sheet.
• need to calculate if you are given the correlation coefficient and need to calculate the standard deviation of a two asset portfolio

Question 12

Correlation/Correlation Coefficient

Answer 12

-correlation ranges from +1 to -1

+1 denotes two assets are perfectly positively correlated.
0 denotes that assets are completely uncorrelated
1 denotes a perfectly negative correlation.

• diversification benefits (reduction of risk) begin anytime correlation is less than 1, best is -1
• correlation and covariants measure the movement of one security relative to that of another.
• represented by greek letter Rho or r

Question 13

Beta

Answer 13

• beta coefficient is a measure of an individual securities volatility relative to that of the market.
• best used for a DIVERSIFIED portfolio
• it measures systematic risk dependent on the volatility of the security relative to that of the market.

Beta of the market is 1

• stock with a beta of 1 will mirror the market in terms of direction, return, and fluctuation.
• stock with beta higher than 1, means stock fluctuates more than the market and greater risk
• stock with beta lower than 1, means stock fluctuates less relative to market movements.
• beta may be calculated with formula or dividing security risk premium by market risk premium

Question 14

CoEfficient of Determination or R-Squared (r2)

Answer 14

• R-squared measures how much of a return is due to the market.
• calculate by squaring the correlation coefficient.
• higher R2, higher percentage of return from the market (systematic risk) and less from unsystematic risk.
• r2 greater than or equal to .70, beta is an appropriate measure of risk.
• r2 is less than .70, beta is not an appropriate measure of risk and standard deviation should be used

Question 15

Coefficient of determination example

Answer 15

Question 16

Portfolio Risk

Answer 16

• also known as portfolio deviation formula or standard deviation of a two asset portfolio.
• uses weight of both securities involved, the deviations of the respective securities and the correlation coefficient of the two securities.

Question 17

Portfolio Risk Example

Answer 17

Question 18

What are Systematic risk?

Answer 18

Systematic risk - it is inherent in the system as a result of the unknown element existing in securities that have no guarantees-

Nondiversifiable risk, market risk, economy based risk,

Question 19

What are unsystematic risk?

Answer 19

• risk that exists in a specific firm or investment that can be eliminated through diversification.

Diversifiable risk, unique risk, company specific risk

Question 20

Types of systematic risk - PRIME

Answer 20

-Purchasing power risk

Risk that inflation will erode the amount of goods and services that can be purchased

-Reinvestment Rate Risk

Risk that an investor will not be able to reinvest at the same rate of return being received. Mainly impacts bonds

-Interest rate risk

The risk that changes in interest rates will impact price of both equities and bonds.

-Market risk

Impacts all securities in the short term
Because the short term ups and downs of the market tend to take all securities in the same direction.

-Exchange rate risk

Is the risk that a change in exchange rates will impact the price of international securities.

Question 21

Types of unsystematic risk - ABCDEFG

Answer 21

Accounting risk 
Business risk 
Country risk 
Default risk 
Executive risk 
Financial risk 
Government/regulation risk 

-accounting risk

The risk associated with an audit firm being to closely tied to the management of a company

-Business Risk

The inherit risk a company faces by operating in a particular industry.

-Country risk

Risk a company faces by doing business in a particular country.

-Default risk

Risk of a company defaulting on their debt payments.

-Executive risk

Risk associated with the moral and ethical character of management running the company

-Financial Risk

Is the amount of financial leverage deployed by the firm. Financial leverage is the ratio of debt to equity the firm has deployed. Higher percentage of debt deployed by the firm, the more risky.

-Government/Regulation Risk

Risk that tariffs or restrictions may be placed on an industry or firm that may impact the firms ability to effectively compete in an industry.

Question 22

Modern portfolio Theory

Answer 22

• the acceptance by an investor of a given level of risk while maximizing expected return objectives.
• investors seek the highest return attainable at any level of risk
• investors want the lowest level of risk at any level of return
• assumption also made that investors are risk averse.

Question 23

Efficient Frontier

Answer 23

• curve that represents the most efficient portfolios in terms of risk-reward relationship.
• portfolios that lie beneath the efficient frontier are inefficient because there is a portfolio that provides more return for that level of risk.
• portfolios that lie above the efficient frontier are considered unattainable.
• when both portfolios are on the efficient frontier neither is better than the other. It depends on the investors risk tolerance when deciding.

Question 24

Efficient frontier example

Answer 24

Compare Portfolio A to Portfolio C: An investor would prefer Portfolio A because it has the same level
of return, but less risk.

Compare Portfolio B to Portfolio C: An investor would prefer Portfolio B because it has a higher level
of return for the same amount of risk.

Compare Portfolio B and Portfolio E: An investor would prefer Portfolio B because of less risk and
more return.

Compare Portfolio A to Portfolio B: Neither portfolio on the efficient frontier is better than any
portfolio that lies on the efficient frontier. It actually depends on the investor’s risk tolerance when
determining which portfolio is preferred on the efficient frontier.

Question 25

Indifference curves and optimal portfolio

Answer 25

- indifference curves represents how much return and investor needs to take on risk. - investor risk averse - steep indifference curve. More return to take on risk - investor risk-seeking - flat indifference curve - less return to take on risk - optimal portfolio - point at which the investors indifference curve is tangent to the efficient frontier.

Question 26

Capital Market Line

Answer 26

- The macro aspect of the capital asset pricing model (CAPM) - specifies relationship between risk and return in all possible portfolios. - becomes the new efficient frontier Portfolios returns should be on the CML Inefficient portfolios are below the CML - not used to evaluate the performance of a single security - uses standard deviation to measure risk

Question 27

Capital market line - example

Answer 27

-The CML intersects the Y-axis at the risk-free rate because an investor with 100% of his assets in the risk-free asset will yield a return but experience no variability (standard deviation). -The CML runs tangent (touches in only one spot) with the efficient frontier at the "optimal portfolio" or the "tangency portfolio." -Before the CML touches the efficient frontier the investor is said to have a security allocation made up of the optimal portfolio mix and is lending a portion of uninvested assets at the risk-free rate. -At the optimal portfolio the investor is fully invested in that portfolio he does not lend anything at the risk-free rate or borrow at that rate. -To the right of the optimal portfolio the investor is said to have borrowed at the risk-free rate to fully invest all capital and borrowed funds in that portfolio.

Question 28

Capital Asset Pricing Model (CAPM) - important need to memorize

Answer 28

- calculates the relationship of risk and return of an individual security using the Beta (b) as its measure for risk. - often referred to as the security market line (SML) equation because it’s inputs and results are used to construct the SML. - market risk premium = how much an investor should be compensated to take on a market portfolio versus a risk-free asset.

Question 29

Security Market Line

Answer 29

- Both CAPM & SML assume an investor should earn a rate of return at least equal to the risk-free rate of return. - SML intersects the y-axis at the risk-free rate of return. - SML uses beta to measure risk, CML uses standard deviation as its measure of risk. - portfolio return above SML, it would be considered undervalued and should be purchased. - portfolio return below SML, it would be considered overvalued and should not be purchased.

Question 30

Information Ratio (excess return)

Answer 30

- relative risk-adjusted performance measure, higher the excess return (information ratio) the better - measures the excess return and consistency provided by a fund manager relative to a benchmark - can be positive or negative depending on the fun’s performance relative to its benchmark.

Question 31

Treynor index

Answer 31

- risk adjusted performance measure - Relative = one Treynor ratio needs to be compared to another Treynor ratio to provide meaning. - measure of how much return was achieved for each unit of risk. Higher the ratio, the better because more return was provided for each unit of risk. - does not indicate wether a portfolio manager has outperformed or underperformed the market. - standardizes portfolio returns for volatility.

Question 32

Treynor ratio - example

Answer 32

Question 33

Sharpe Index

Answer 33

- Risk adjusted performance measure - Relative = one sharpe ratio needs to be compared to another to provide meaning. - measures how much return was achieved for each unit of risk. - higher the sharpe ratio, the better because that means more return was provided for each unit of risk. - measures risk premiums relative to the total amount of risk in the portfolio. - does not measure a portfolio managers performance against the market.

Question 34

Jensen Model or Jensens Alpha

Answer 34

-difference from sharpe and treynor - capable of distinguishing a managers performance relative to that of the market. & Differences between realized or actual returns and required returns as specificied by CAPM - absolute performance on a risk adjusted basis. Other two are relative performance (sharpe & treynor) - DOES measure a portfolio managers performance against that of the market

Question 35

Jensens alpha - calculation and absolute performance

Answer 35

- an absolute performance measure simply means looking at Jensens alpha tells you something. - alpha - indicative of the level of a managers performance - a positive alpha = fund manager provided more return than was expected for the risk undertaken - a negative alpha = fund manager provides less return than was expected for risk undertaken - alpha of 0 = fund manager provided a return equal to the return that was expected for the risk undertaken

Question 36

Jensens Alpha - Example

Answer 36

Question 37

Which risk adjusted performance to use Sharpe, Treynor, or Alpha?

Answer 37

- well diversified portfolio = r-squared is greater or equal to .70 = Beta appropriate measure of risk = use Treynor and Alpha as they use Beta - not well diversified portfolio = r-squared less than .70 = standard deviation appropriate measure of risk = use Sharpe as it uses standard deviation

Question 38

Summary of performance measures

Answer 38

Question 39

What is total risk?

Answer 39

Total risk = Systematic + unsystematic risk Total risk is measured by standard deviation Systematic risk is measured by beta