Portfolio Management Level 1

If an investor bought a stock for $32 and sold it one year later for $37.50 after receiving $2 in dividends, what was the holding period return on this investment?

23.44% HPR = [D + End Price - Beg Price] / Beg Price HPR = [2 + 37.50 - 32] / 32 = 0.2344.

In a five-year period, the annual returns on an investment are 5%, -3%, -4%, 2%, and 6%. The standard deviation of annual returns on this investment is closest to:

4.5% mean annual return = (5% − 3% − 4% + 2% + 6%) / 5 = 1.2% Squared deviations from the mean: 5% − 1.2% = 3.8% 3.8^2 = 14.44 -3% -1.2% = -4.2%. -4.2^2 = 17.64 -4% -1.2% = -5.2%. -5.2^2 = 27.04 2% -1.2% = 0.8%. 0.8^2 = 0.64 6% -1.2% = 4.8%. 4.8^2 = 23.04 sum of squared deviations = 14.44 + 17.64 + 27.04 + 0.64 + 23.04 = 82.8 sample variance = 82.8 / (5 − 1) = 20.7 sample standard deviation = 20.7^1/2 = 4.55%

One study showed that it only took about 12 to 18 stocks in a portfolio to achieve

90% of the maximum diversification possible. Another study indicated it took 30 securities. Whatever the number, it is significantly less than all the securities. Note, in the figure, that once you get to 30 or so securities in a portfolio, the standard deviation remains constant. The remaining risk is systematic, or nondiversifiable, risk.

Stock A has a standard deviation of 10.00. Stock B also has a standard deviation of 10.00. If the correlation coefficient between these stocks is - 1.00, what is the covariance between these two stocks?

= (- 1.00)(10.00)(10.00) = -100.00.

Treynor Measure

= Rp - Rf / Bp excess return per unit of systematic risk Portfolios that lie above the SML have treynor measures greater than those of any security or portfolio that lies along the SML and also have positive Jenses Alpha

Jensons Alpha

= Rp - [Rf + Bp(Rm-Rf)] = percentage portfolio return above that of a portfolio with the same beta as the portfolio that lies on the SML

Expected return of the portfolio

= WAE(RA) + WBE(RB)

Covariance

= [Rt1- R1] [ Rt2-R2] / n-1 Rt1= return on asset 1 in period t Rt2= return on asset 2 in period t R1= mean return on asset 1 R2= mean return on asset 2 n = # of periods

Sharpe Ratio

= excess returns per unit of total portfolio risk Higher sharpe ratios indicate better risk-adj portfolio performance (When evaluating the performance of a portfolio with risk that differs from that of a benchmark portfolio we need to adjust the active portfolio returns risk) = E[R portfolio] - Rf / std. dev. of portfolio Sharpe ratio is based on total risk (std. dev.) rather than systematic risk (beta)

Variance of a portfolio

= std dev of portfolio std. dev of portfolio = so Sq. root of Variance of portfolio

total risk =

= systematic risk + unsystematic risk The concept of systematic risk applies to individual securities as well as to portfolios. Some securities' returns are highly correlated with overall market returns. Examples of firms that are highly correlated with market returns are luxury goods manufacturers such as Ferrari automobiles and Harley Davidson motorcycles. These firms have high systematic risk (i.e., they are very responsive to market, or systematic, changes). Other firms, such as utility companies, respond very little to changes in the systematic risk factors. These firms have very little systematic risk.

What is the required rate of return for a stock with a beta of 1.2, when the risk-free rate is 6% and the market risk premium is 12%?

=20.4% = 6+ 12 x 1.2 = 6+ 14.4 =20.4

For an asset with a current price of 100, which of the following price targets is most likely based on a Fibonacci ratio?

161.80. The value 1.618 is the ratio of large consecutive Fibonacci numbers. Technical analysts who employ Elliott wave theory frequently use Fibonacci ratios to set price targets.

The covariance of the market's returns with a stock's returns is 0.005 and the standard deviation of the market's returns is 0.05. What is the stock's beta?

2.0 beta = covariance / market variance Mkt variance= 0.05^2 = 0.0025 beta = 0.005/ 0.0025 Beta = 2.0

The capital allocation line is a straight line from the risk-free asset through:

the optimal risky portfolio.

An investor buys one share of stock for $100. At the end of year one she buys three more shares at $89 per share. At the end of year two she sells all four shares for $98 each. The stock paid a dividend of $1.00 per share at the end of year one and year two. What is the investor's time-weighted rate of return?

0.06% The holding period return in year one is ($89.00 - $100.00 + $1.00) / $100.00 = -10.00%. The holding period return in year two is ($98.00 - $89.00 + $1.00) / $89 = 11.24%. The time-weighted return is [{1 + (-0.1000)}{1 + 0.1124}]1/2 - 1 = 0.06%.

Assets A (with a variance of 0.25) and B (with a variance of 0.40) are perfectly positively correlated. If an investor creates a portfolio using only these two assets with 40% invested in A, the portfolio standard deviation is closest to:

0.5795 = = [(0.4)^2(0.25) + (0.6)^2(0.4) + 2(0.4)(0.6)1(0.25)^0.5(0.4)^0.5]^0.5 = 0.5795

Variance of a portfolio

1. Standard deviation squared 2. The weight of the securities in the portfolio (w1,w2) 3. The standard deviation of the stock's returns 4. The correlation between the returns on the securities 5. = w1^2*SD(R1)^2 + W2^2*SD(R2)^2 + 2w1w2*SD(R1)*SD(R2)*Corr(1,2) 6. Nonlinear function

2 measures of portfolio performance based on systematic (beta) risk rather than total risk are

1. Treynor Measure (measure of slope) 2. Jensen's Alpha (measure of percentage returns in excess)

A portfolio to the right of the market portfolio on the CML is:

A borrowing portfolio A portfolio to the right of a portfolio on the CML has more risk than the market portfolio. Investors seeking to take on more risk will borrow at the risk-free rate to purchase more of the market portfolio. (LOS 53.b)

Correlation

A measure of the extent to which two factors vary together, and thus of how well either factor predicts the other. p1,2 = Cov1,2/ o1 o2 p1,2 = correlation coefficient ( bound by -1 and +1) o1,2 = std. deviation

Which of the following technical analysis observations most likely represents a change in polarity?

A resistance level on a line chart is breached and later acts as a support level. "Change in polarity" refers to a perceived tendency for breached support levels to become resistance levels and breached resistance levels to become support levels.

A leveraged return

A return that is a multiple of the return on the underlying asset is calculated as the gain or loss on the investment as a percentage of an investor's cash investment.

Two Fund Separation Theorem

All investors' optimum portfolios will be made up of some combination of an optimal portfolio of risky assets and a risk free asset (capital allocation line)

Attribution Analysis

An analysis of the sources of returns differences between active portfolio returns and those of a passive benchmark portfolio..is part of performance evaluation

Risk

Buying insurance transfers a risk to the insurance company. Shifting a risk is changing the distribution of outcomes, typically with a derivatives contract. Preventing a risk refers to taking steps such as strengthening security procedures.

An investor put 60% of his portfolio into a risky asset offering a 10% return with a standard deviation of returns of 8% and put the balance of his portfolio in a risk-free asset offering 5%. What is the expected return and standard deviation of his portfolio?

Expected return: (0.60 × 0.10) + (0.40 × 0.05) = 0.08, or 8.0%. Standard deviation: 0.60 × 0.08 = 0.048, or 4.8%. (LOS 53.a)

One multifactor model that is often used is that of

Fama and French. They estimated the sensitivity of security returns to three factors: firm size, firm book value to market value ratio, and the return on the market portfolio minus the risk-free rate (excess return on the market portfolio). Carhart suggests a fourth factor that measures price momentum using prior period returns. Together, these four factors do a relatively good job of explaining returns differences for U.S. equity securities over the period for which the model has been estimated.

A 10% coupon bond was purchased for $1,000. One year later the bond was sold for $915 to yield 11%. The investor's holding period yield on this bond is closest to:

HPY = [(interest + ending value) / beginning value] - 1 = [(100 + 915) / 1,000] - 1 = 1.015 - 1 = 1.5%

When preparing a strategic asset allocation, how should asset classes be defined with respect to the correlations of returns among the securities in each asset class?

High correlation within asset classes and low correlation between asset classes.

The optimal portfolio in the Markowitz framework occurs when an investor achieves the diversified portfolio with the:

Highest utility

M-squared

Measure produces the same portfolio rankings as the Sharpe Ratio but is stated in percentage terms. = (Rp - Rf) (std.dev M / std. dev. portfolio) - (Rm-Rf) A measure of risk-adj performance the additional return that could have been earned by leveraging the active portfolio so that its risk = to the mkt portfolio

Multifactor models The general form of a multifactor model with k factors is as follows:

Multifactor models most commonly use macroeconomic factors such as GDP growth, inflation, or consumer confidence, along with fundamental factors such as earnings, earnings growth, firm size, and research expenditures. = E(Ri) − Rf = βi1 × E(Factor 1) + βi2 × E(Factor 2) + ....+ βik × E(Factor k) This model states that the expected excess return (above the risk-free rate) for Asset i is the sum of each factor sensitivity or factor loading (the βs) for Asset i multiplied by the expected value of that factor for the period.

Real return

Return adjusted for inflation Real return measures the increase in an investor's purchasing power: how much more goods she can purchase at the end of one year due to the increase in the value of her investments.

Active Portfolio Management

Such investors will not use the weights of the market portfolio but will invest more than the market weights in securities that they believe are undervalued and less than the market weights in securities which they believe are overvalued.

market risk premium.

The difference between the expected return on the market and the risk-free rate

Which of the following statements about an organization's risk tolerance is most accurate?

The financial strength of an organization is one of the factors it should consider when determining its risk tolerance.

Global Minimum Variance Portfolio

The portfolio on the efficient frontier with the least risk

Beta

The sensitivity of an asset's return to the return on the market index in the context of the market model is referred to as its beta. Beta is a standardized measure of the covariance of the asset's return with the market return. = Covariance of Asset i's return with the market return / variance of the market return

An Elliott wave theorist who forecasts prices based on Fibonacci ratios is most likely to predict that a wave will be:

The sequence of Fibonacci numbers is 0, 1, 1, 2, 3, 5, 8, 13... . Five-eighths is a Fibonacci ratio.

What is the risk measure associated with the capital market line (CML)?

Total Risk

capital market line (CML)

Under the assumption of homogeneous expectations, this optimal CAL for all investors E(Rp) = Rf + [E(Rm) - Rf / std. dev. M ) x Std. Dev Portfolio The y-intercept of this line is Rf Slope = [E(Rm) - Rf / std. dev. M )

An investor buys a share of stock for $40 at time t = 0, buys another share of the same stock for $50 at t = 1, and sells both shares for $60 each at t = 2. The stock paid a dividend of $1 per share at t = 1 and at t = 2. The periodic money-weighted rate of return on the investment is closest to:

Using the cash flow functions on your financial calculator, enter CF0 = -40; CF1 = -50 + 1 = -49; CF2 = 60 × 2 + 2 = 122; CPT IRR = 23.82%. (Module 52.1, LOS 52.a)

An investor begins with a $100,000 portfolio. At the end of the first period, it generates $5,000 of income, which he does not reinvest. At the end of the second period, he contributes $25,000 to the portfolio. At the end of the third period, the portfolio is valued at $123,000. The portfolio's money-weighted return per period is closest to:

Using the financial calculator, the initial investment (CF0) is -100,000. The income is +5,000 (CF1), and the contribution is -25,000 (CF2). Finally, the ending value is +123,000 (CF3) available to the investor. Compute IRR = 0.94

A momentum indicator based on the ratio of price increases to price decreases over the last 14 days is most likely a:

a Relative Strength Index.

Bruce Johansen, CFA, is fully invested in the market portfolio. Johansen desires to increase the expected return from his portfolio. According to capital market theory, Johansen can meet his return objective by:

borrowing at the risk-free rate to invest in the risky market portfolio.

In a defined benefit pension plan:

the plan sponsor promises a predetermined retirement income to participants.

When comparing portfolios that plot on the security market line (SML) to those that plot on the capital market line (CML), a financial analyst would most accurately state that portfolios that lie on the SML:

are not necessarily well diversified, while portfolios on the CML are well diversified. Although the risk measure on the capital market line diagram is total risk, all portfolios that lie on the CML are well diversified and have only systematic risk. This is because portfolios on the CML are all constructed from the risk-free asset and the (well-diversified) market portfolio. Any portfolio, including single securities, will plot along the SML in equilibrium. Their unsystematic risk can be significant, but it is not measured on the SML diagram because unsystematic risk is not related to expected return. Both the CML and the SML reflect relations that hold when prices are in equilibrium.

All portfolios on the capital market line:

are perfectly positively correlated.

As the number of stocks in a portfolio increases, the portfolio's systematic risk:

can increase or decrease When you increase the number of stocks in a portfolio, unsystematic risk will decrease at a decreasing rate. However, the portfolio's systematic risk can be increased by adding higher-beta stocks or decreased by adding lower-beta stocks. (LOS 53.c)

A line that represents the possible portfolios that combine a risky asset and a risk free asset is most accurately described as a:

capital allocation line.

Given the following data, what is the correlation coefficient between the two stocks and the Beta of stock A? standard deviation of returns of Stock A is 10.04% standard deviation of returns of Stock B is 2.05% standard deviation of the market is 3.01% covariance between the two stocks is 0.00109 covariance between the market and stock A is 0.002

correlation coefficient = 0.00109 / (0.0205)(0.1004) = 0.5296. beta of stock A = covariance between stock and the market / variance of the market Beta = 0.002 / 0.03012 = 2.2

Examples of financial risks include:

credit risk, market risk, and liquidity risk.

The money-weighted return

defined as the internal rate of return on a portfolio, taking into account all cash inflows and outflows. The beginning value of the account is an inflow, as are all deposits into the account. All withdrawals from the account are outflows, as is the ending value.

Generally, a resistance level tends to develop after a stock has

experienced a steady decline from a higher price level. Technicians believe that the decline in price will cause some investors who acquired the stock at a higher price to look for an opportunity to sell it near their break-even points. Therefore, the supply of stock owned by investors is overhanging the market

For asset allocation purposes, asset classes should be specified such that correlations of returns are relatively:

high within each asset class and low among asset classes. Asset classes should be defined such that correlations of returns within the asset class are relatively high (because assets within a class should perform alike over time), while correlations of returns among asset classes are relatively low (to benefit from diversification). (LOS 54.f)

The optimal portfolio for each investor is the

highest indifference curve that is tangent to the efficient frontier.

In determining the appropriate asset allocation for a client's investment account, the manager should:

incorporate forecasts of future economic conditions.

The geometric mean return

is a compound annual rate. When periodic rates of return vary from period to period, the geometric mean return will have a value less than the arithmetic mean return: n sq root (1+r1) x (1+ r2) x (1+ r3) x (1+rn) - 1

Holding period return (HPR)

is simply the percentage increase in the value of an investment over a given time period: = end of period value / beginning of period value - 1 = Pt + Divt/ P0 -1

The arithmetic mean return

is the simple average of a series of periodic returns. It has the statistical property of being an unbiased estimator of the true mean of the underlying distribution of returns: = (r1+ r2 + r3 + rn) / n

Time-weighted rate of return

measures compound growth. it is the rate at which $1 compounds over a specified performance horizon. Time-weighting is the process of averaging a set of values over time. In the investment management industry, the time-weighted rate of return is the preferred method of performance measurement, because it is not affected by the timing of cash inflows and outflows.

In a defined contribution pension plan:

the employee accepts the investment risk. The plan sponsor and manager neither promise a specific level of retirement income to participants nor make investment decisions. These are features of a defined benefit plan. (LOS 51.d)

A portfolio currently holds Randy Co. and the portfolio manager is thinking of adding either XYZ Co. or Branton Co. to the portfolio. All three stocks offer the same expected return and total risk. The covariance of returns between Randy Co. and XYZ is +0.5 and the covariance between Randy Co. and Branton Co. is -0.5. The portfolio's risk would decrease:

more if she bought Branton Co.

if a stock's relative strength ratio increases, the stock is:

outperforming its benchmark. if the relative strength ratio (stock price / benchmark value) increases, the stock is outperforming the benchmark stock or index against which it is being measured. This does not imply that the stock is increasing in price; if the stock price decreases but the benchmark decreases by a larger percentage, the ratio will increase. Volume is not an input into a relative strength ratio.

A stock with a beta of 0.7 currently priced at $50 is expected to increase in price to $55 by year-end and pay a $1 dividend. The expected market return is 15%, and the risk-free rate is 8%. The stock is:

overpriced, so do not buy it. required rate = 8 + 0.7(15 − 8) = 12.9% return on stock = (55 − 50 + 1) / 50 = 12% The stock falls below the SML so it is overpriced. (LOS 53.h)

Efficient frontier

portfolios that have the greatest expected return for each level of risk (std. dev)

Minimum Variance Portfolio

portolios with the lowest std. dev of all portfolios with a given expected return

A portfolio manager uses a computer model to estimate the effect on a portfolio's value from both a 3% increase in interest rates and a 5% depreciation in the euro relative to the yen. The manager is most accurately described as engaging in:

scenario analysis.

The variance of returns is 0.09 for Stock A and 0.04 for Stock B. The covariance between the returns of A and B is 0.006. The correlation of returns between A and B is:

sq root of 0.09 = 0.30 sq root of 0.04 = 0.20 correlation =0.006/(0.30)(0.20) = 0.10

Sample variance

s² Look at formula in book page 98

Value-at-Risk (VaR) and Conditional VaR are best described as measures of:

tail risk. the probability of or magnitude of extreme negative outcomes in the tail of a distribution.

Security Market Line

the return line that reflects the attitudes of investors regarding the minimum acceptable return for a given level of systematic risk associated with a security in CAPM world, all properly priced securities and portfolios of securities will plot on the SML shows the equilibrium (required) return for any security or portfolio based on its beta (systematic risk) If the estimated return plots over the SML the security is under valued. Any stock not plotting on the SML is mispriced

An inverse head and shoulders pattern most likely indicates:

the reversal of a downtrend.

The risk-free rate is 6%, and the expected market return is 15%. A stock with a beta of 1.2 is selling for $25 and will pay a $1 dividend at the end of the year. If the stock is priced at $30 at year-end, it is:

underpriced, so buy it. required rate = 6 + 1.2(15 − 6) = 16.8% return on stock = (30 − 25 + 1) / 25 = 24% Based on risk, the stock plots above the SML and is underpriced, so buy it. (LOS 53.h)

A simplified form of a single-index model is the market model,

which is used to estimate a security's (or portfolio's) beta and to estimate a security's abnormal return (return above its expected return) based on the actual market return. Ri = αi + βiRm + ei where: Ri = return on Asset i Rm = market return βi = slope coefficient αi = intercept ei = abnormal return on Asset i

A more risk averse investor

will have a steeper indifference curve reflecting higher risk aversion coefficient

Population variance

σ² Look at formula in book page 98