Volume 2 & 6 - Portfolio Management Flashcards
Portfolio Risk and Return: Part 1
describe characteristics of the major asset classes that investors consider in forming portfolios
explain risk aversion and its implications for portfolio selection
explain the selection of an optimal portfolio, given an investor’s utility (or risk aversion) and the capital allocation line
calculate and interpret the mean, variance, and covariance (or correlation) of asset returns based on historical data
calculate and interpret portfolio standard deviation
describe the effect on a portfolio’s risk of investing in assets that are less than perfectly correlated
describe and interpret the minimum-variance and efficient frontiers of risky assets and the global minimum-variance portfolio
Historical returns document past performance, while expected returns reflect anticipated future performance. An asset’s expected return is a function of the real risk-free rate, expected inflation, and any risk premiums that investors require as compensation.
Using a mean and variance approach assumes that returns are normally distributed and that markets are informationally and operationally efficient.
However, these assumptions do not necessarily hold.
A normal distributions has three characteristics:
Its mean and median are equal.
It is completely defined by its mean and variance
It is symmetric around its mean.
Most equity return distributions are not normally distributed. They are often asymmetric (or skewed). Stock returns are usually negatively skewed
Distributions also usually have fatter tails than normally distributed variables, which means extreme returns are more likely. This is referred to as kurtosis
The presence of skewness and/or kurtosis is contrary to the assumption that returns are normally distributed. The assumption that markets are operationally efficient is limited by market frictions, such as trading costs. These frictions impact both actual and expected returns.
Risk-seeking investors enjoy the thrill of gambling and will take risks even with a negative expected return.
Risk-neutral investors only care about the expected return. They will prefer an investment that offers a higher return, regardless of its level of risk.
Risk-averse investors will choose the investment that offers the highest return for their desired level of risk (or the least risk for their desired level of return). It is reasonable to assume that most investors are risk-averse.
The key conclusions from utility functions are:
1- Utility has no maximum or minimum
2- A higher return contributes to higher utility
3- Higher variance reduces utility (for risk-averse investors)
4- Utility is only useful in ranking investment options
Utility measures the relative satisfaction gained from a particular portfolio. The utility that investors derive from an asset or portfolio is a function of their degree of risk aversion (A), which is the marginal reward that they require as compensation for taking an additional unit of risk.
The value of A will be positive for risk-averse investors and higher for investors with lower levels of risk tolerance.
A = 0 for risk neutral
A < 0 for risk seeking (ignorant)
Indifference curves plot the risk-return pairs that have the same utility.
The capital allocation line (CAL) represents the investment options for this portfolio of two securities. It is the plot of different risk-return combinations derived by changing the weights of the two securities.
The CAL represents all the investment options. An investor must be somewhere on the line.
The slope represents the additional return required for every increment in risk, which is the market price of risk. The slope is equivalent to the Sharpe ratio.
Indifference curves can be used to determine the optimal investment point on the CAL. The goal is to maximize utility, which is the same as getting on the highest indifference curve. This optimal investment corresponds to the point of tangency between the indifference curve and the capital allocation line.
With respect to risk-averse investors, a risk-free asset will generate a numerical utility that is:
A
the same for all individuals.
B
positive for risk-averse investors.
C
equal to zero for risk seeking investors.
A
When p12 = 1 , the two assets are perfectly positively correlated. An asset is always perfectly positively correlated with itself. If a portfolio is composed of two assets are perfectly positively correlated with each other, its standard deviation is a simple weighted average of the standard deviations of the individual assets.
The lower correlation between two assets in a portfolio, the higher the expected return for a given level of portfolio risk.
If p12 = 0 , the two assets are uncorrelated. The return on the risk-free asset is known in advance with certainty, meaning that it has zero volatility. It follows that the correlation between the risk-free asset and any risky asset is zero. Adding the risk-free asset to a portfolio of risky assets will lower the portfolio’s riskiness as measured by standard deviation.
The power of diversification is its ability to reduce portfolio volatility. There are many ways to diversify a portfolio, notably by making allocations across asset classes (e.g., large-cap stocks, small-cap stocks, corporate bonds, government bonds). Other ways to achieve diversification include:
- Holding international assets, which provides the additional benefit of diversifying currency risk exposure
- Using index funds as a relatively inexpensive and more efficient means of diversification
- Avoiding ownership of your employer’s stock to limit dependence on the source of your employment income to provide investment income as well
- Protecting risky assets by purchasing insurance, which has a negative expected return but is also perfectly negatively correlated with the protected asset
As more assets are added to a portfolio of risky assets, its variance approaches the average covariance of its components.
Each asset that is being considered for inclusion in a portfolio should be evaluated in the portfolio context. Specifically, an asset should only be added to a portfolio if its Sharpe ratios is greater than the Sharpe ratio of the existing portfolio multiplied by the portfolio’s correlation with the new asset
As the number of assets in an equally-weighted portfolio increases, the contribution of each new asset’s variance to the portfolio’s overall variance most likely:
A
increases.
B
approaches zero.
C
remains unchanged.
B
Efficient frontier:
Adding less-correlated asset classes (e.g., international assets) will improve the risk-return trade-off, pushing the curve up and to the left.
The minimum-variance frontier is the left edge of the possibilities in the graph below. It represents the least portfolio risk that can be obtained for a given expected return. The global minimum-variance portfolio, located on the far left of the curve, is the least risky of the minimum variance portfolios.
The section of the minimum-variance frontier that lies above the global minimum-variance portfolio is the Markowitz efficient frontier. Risk-averse investors will not consider portfolios on the lower half of the minimum-variance frontier because, for any portfolio that plots in this section, there is a Markowitz efficient frontier that offers a higher expected return for the same level of risk.
According to the two-fund separation theorem, all investors will use the risky portfolio P to a greater or lesser extent depending on their level of risk aversion. Investors will have different allocations to the risk-free asset, but they will all create portfolios that use the optimal portfolio,
P , and plot on the CAL according to their risk tolerance. Note that CAL portfolios offer better risk-return profiles than efficient frontier portfolios of equivalent risk that have not been combined with the risk-free asset.
The portfolio, P , is the optimal risky portfolio.
Tangent of CAL with Efficient frontier
The location of an investor’s optimal portfolio on the CAL will be at its point of tangency with their indifference curve.
A less risk-averse investor could create a portfolio that plots above P by borrowing at the risk-free rate and investing the proceeds in the optimal risky portfolio (e.g., allocations of -20% to the risk-free asset and 120% to portfolio P ).
Portfolio Risk and Return: Part 2
describe the implications of combining a risk-free asset with a portfolio of risky assets
explain the capital allocation line (CAL) and the capital market line (CML)
explain systematic and nonsystematic risk, including why an investor should not expect to receive additional return for bearing nonsystematic risk
explain return generating models (including the market model) and their uses
calculate and interpret beta
explain the capital asset pricing model (CAPM), including its assumptions, and the security market line (SML)
calculate and interpret the expected return of an asset using the CAPM
describe and demonstrate applications of the CAPM and the SML
calculate and interpret the Sharpe ratio, Treynor ratio, M2, and Jensen’s alpha
Each individual investor will make portfolio decisions that are consistent with their own willingness and ability to tolerate risk. Investors with higher levels of risk aversion will build portfolios with greater allocations to less risky assets, notably the risk-free asset.
However, capital market theory also stipulates that even investors who are willing to accept the highest levels of risk should use the risk-free asset in their portfolios. The risk-free asset’s value in a portfolio stems from the fact that its returns are completely uncorrelated with those of risky assets.
Capital market theory further shows that the capital allocation line created by combining the risk-free asset with a portfolio of risky assets allows for portfolios that dominate those on efficient frontier for all levels of risk tolerance. An investor’s optimal portfolio of risky assets is the one on the CAL that intersects with their indifference curve. All else equal, investors prefer a steeper CAL for a given risk-free rate because this maximizes their expected return for their level of risk tolerance.
Capital market theory assumes homogeneity of expectations, meaning that all investor have the same economic expectations about investment characteristics such as prices, cash flows, and discount rates for all assets. If this assumption holds, all investors will conduct the same analysis, which should produce the same optimal portfolios of risky assets.
In reality, this assumption does not hold. However, if we accept market prices as proxies for the valuations that would exist under homogenous expectations, it is possible to use these as the basis for asset weights in a market portfolio that is the optimal portfolio of risky assets for all investors.
Active investors believe that various market inefficiencies cause assets to trade at prices that do not reflect their true value.
Overweighted the undervalued and sold short the overvalued.
The “market” portfolio includes all risky assets. In theory, this can includes anything that has value, such as traditional assets (e.g., stocks), alternative assets (e.g., real estate), and even intangible assets (e.g., human capital). In practice, investors limit their definition of the market portfolio to include assets that are valuable, tradable, and investable. For example, a stock that is listed on a local exchange with prohibitions on trading by foreigners would be considered valuable and tradable, but not investable.
Commonly used: S&P 500
The capital market line (CML) is simply a capital allocation line with the risky portfolio being the market portfolio. Graphically, it is the line tangent to the efficient frontier constructed from all available risky assets.
Investors can leverage positions by borrowing at the risk-free rate Rf and investing the proceeds in the market portfolio M
However, while investors can easily lend as the risk-free rate by purchasing short-term government bills, they cannot borrow at the same rate. Because investors must pay a higher borrowing rate Rb , the CML will become kinked at M with a change in slope to reflect the different rates at which investors can borrow and lend.
Which of the following statements most accurately defines the market portfolio in capital market theory? The market portfolio consists of all:
A
risky assets.
B
tradable assets.
C
investable assets.
A
Systematic risk is also called non-diversifiable risk or market risk. It includes risks like interest rates and economic cycles that cannot be avoided. Nonsystematic risk is also called company-specific, industry-specific, or diversifiable risk. Diversification can reduce or even eliminate nonsystematic risk.
Since nonsystematic risk can be eliminated with a diversified portfolio, investors should not receive compensation for it. Investors are only compensated for systematic risk.
A return-generating model estimates the expected return of a given security. Multi-factor models allow for more than one variable. The factors could be macroeconomic, fundamental, or statistical, although statistical variables that have no macroeconomic or fundamental meaning are usually discarded.
A single-index model generated return expectations using an asset’s sensitivity to a market index as the only factor. Because of its simplicity, the single-index model can be used to create the capital market line (CML).
The market model is the most common implementation of the single-index model. It is similar to the single-index model, but it allows for an easier estimation of beta.
Beta measures the sensitivity of an asset’s return to the market return. It is the covariance between the security return and the market return divided by the market variance.
Beta can be estimated by using the market model with historical regression. Beta represents the slope of the best-fit line when plotting the market return on the horizontal axis and the security return on the vertical axis
The historical beta may not accurately represent future systematic risk.
Assumptions of the CAPM
1- Investors are risk-averse, utility-maximizing, and rational individuals :
Investors expect compensation for taking risk and always seek more wealth. Investors correctly evaluate available information.
2- Markets are frictionless – no taxes or transaction costs :
This also includes being able to borrow and lend at the same risk-free rate. There are no extra costs or restrictions on short-selling.
3- All investors plan for same single holding period
4- Investors have homogeneous expectations :
Rational investors will arrive at the same conclusions regarding valuations since the inputs are the same. This leads to the same optimal risky portfolio for all investors.
5- Investments are infinitely divisible
6- Investors are price takers :
No investor is large enough to influence the prices.
The security market line (SML) is constructed with beta on the horizontal axis and expected return on the vertical axis. The slope is the market risk premium,
Rm - Rf. The SML applies to any security, not just efficient portfolios.
The security market line also applies to a portfolio of securities. The portfolio beta is simply the weighted average of the individual betas.
CAPM can be used to estimate the expected return or cost of capital. These rates can then be used to calculate the present value of expected cash flows.
With respect to the capital asset pricing model, the market risk premium is:
A
less than the excess market return.
B
equal to the excess market return.
C
greater than the excess market return.
B
With respect to the security market line (SML), which of the following is most accurate?
A
The SML only applies to efficient portfolios
B
The slope of the SML is the market risk premium
C
The SML is a graphical illustration of the efficient frontier
B
Theoretical Limitations of the CAPM
1- It is a single-factor model that only includes beta risk.
2- It is a single-period model that does not consider multi-period implications of decisions.
Practical Limitations of the CAPM
1- The true market portfolio includes all assets, some of which are not investable.
2- Proxies for the market portfolio can generate different return estimates.
3- Beta risk estimates require a long history but may not be applicable for future risk estimates.
4- CAPM is a poor predictor of returns.
5- Homogeneity of investor expectation is assumed to generate a single optimal risky portfolio.
Treynor Ratio:
This is like the Sharpe ratio, but it substitutes beta risk for total risk. Like the Sharpe ratio, it is only meaningful if both the numerator and denominator are positive.
Sharpe Ratio :
This reward-to-variability ratio is the slope of the capital allocation line. It is an easy measure to use, but it suffers from two shortcomings:
The Sharpe ratio uses total risk rather than systematic risk.
The ratio is meaningless but for comparisons with other Sharpe ratios.
M-Squared :
M-squared was created by Franco Modigliani and his granddaughter, Leah. It is based on total risk like the Sharpe ratio. The portfolio return is adjusted to what it would be at the same risk level as the market. If M2 is greater than the market return, then the portfolio outperformed the market on a risk-adjusted basis.
Jensen’s Alpha :
As with the Treynor ratio, this measure is based on systematic risk. It is the difference between the actual return and risk-adjusted return using beta. Portfolios that outperform the market will have a positive
Both Sharpe and Treynor ratios are commonly used to rank portfolios. On the other hand, M-squared and Jensen’s alpha provide direct information on whether the portfolio has outperformed the market.
The security characteristic line (SCL) is a plot of the excess return of the security to the excess return of the market. The slope is beta and the intercept is alpha.
Individual price calculations could differ from the CAPM-calculated price (heterogeneous beliefs). If the investor-calculated price is higher, the asset is considered undervalued. A positive Jensen’s alpha indicates a good buy. Undervalued securities are candidates for investments and will plot above the security market line.
Based on CAPM, investors should hold a combination of the risk-free asset and the risky market portfolio. It is not practical or necessary to own every existing risky security. Non-systematic risk can be effectively eliminated with about 30 individual securities.
An investor could start with an index such as the S&P 500. Other securities with positive a could be included. Also, securities in the S&P 500 with negative a could be dropped and ones with positive could be increased in weight. A security with a larger information ratio (i.e., alpha divided by the nonsystematic risk) is more valuable.
Portfolio Management: An Overview
describe the portfolio approach to investing
describe the steps in the portfolio management process
describe types of investors and distinctive characteristics and needs of each
describe defined contribution and defined benefit pension plans describe aspects of the asset management industry
describe mutual funds and compare them with other pooled investment products
If the portfolio standard deviation is only 14% rather than the 20% average, the portfolio’s diversification ratio is 70% (14%/20%).
The optimal portfolio will maximize the return for a given amount of risk or minimize the risk for a given level of return.
However, severe market turmoil often leads to many assets moving down in value together. This phenomenon, known as contagion, reduces the benefits of diversification that are achieved under normal market conditions.
No downside protection
All else equal, adding a security with returns that are negatively correlated with those of an equally-weighted portfolio will most likely:
A
decrease the diversification ratio.
B
increase the diversification ratio.
C
not impact the diversification ratio.
A
The diversification ratio of an equally-weighted portfolio is the ratio of the portfolio’s standard deviation to the average standard deviation of its components.
MPT emphasizes focus on the portfolio rather than individual securities in isolation. The implication is that investors should focus only on systematic, or non-diversifiable, risk. There is no reward to be earned for accepting risk that can be eliminated by diversifying a portfolio’s assets. This perspective on risk is the basis for the capital asset pricing model (CAPM).
The portfolio management process has three steps:
- The Planning Step
Understanding the client’s needs
Preparing the Investment Policy Statement (IPS) - The Execution Step
Asset allocation
Security analysis
Portfolio construction - The Feedback Step
Monitoring and rebalancing
Performance measurement and reporting
The IPS may specify a benchmark, such as a market index, that can be used to measure and evaluate the manager’s performance.
The portfolio that emerges from the execution step should reflect target weights for asset classes, any individual assets that were identified in the security analysis process, and the client’s level of risk tolerance. Investment decisions should be made based on consideration of the entire portfolio rather than an isolated focus on individual assets. Managers may rely on the services of outside specialists, such as buy-side traders, to execute the necessary transactions.
Any analysis of a portfolio’s performance should be done relative to a relevant benchmark that has been specified in the IPS.
University endowments and charitable foundations provide ongoing financial support to their affiliated organizations. Usually, their investment objective is to earn sufficient returns to maintain the real (inflation-adjusted) value of their assets after meeting their annual spending commitments. As a general rule, endowments and foundations expect to operate indefinitely, which gives them very long investment horizons and high risk tolerance. Liquidity needs are usually relatively low as a share of assets.
Banks : Risk tolerance is low and liquidity needs are high because deposits can be redeemed on demand. Note that deposits made by customers are assets that belong to the customers and are therefore liabilities for the banks. Because customers could withdraw their funds, banks must maintain a portfolio of liquid assets to offset this liability. These assets are known as reserves, which are typically invested in low-risk, short-term fixed-income securities.
Often, DB pension plans hold long-term bonds to offset their liabilities and generate income (which is particularly important for more mature plans). Long investment horizons and low liquidity needs contribute to a relatively high level of risk tolerance.
The time horizon is effectively indefinite if new members are continually being admitted into the pension plan. Because a steady inflow of new participants is accompanied by a corresponding inflow of contributions, current income needs are low in these circumstances.
If the plan was closed, the time horizon would still be relatively long but finite.
Life insistance companies typically have longer horizons than non-life companies, but liquidity needs are still relatively high and risk tolerance is relatively low. Income needs are low compared to, for example, a mature-stage DB pension plan.
Non-life (property and casualty) insurance companies need to be able to pay liabilities for claims on an ongoing basis. In order to be able to meet these obligations, their investments tend to be relatively short-term, liquid, and conservative.
Investment companie : liquidity needs are generally high in order to be able to meet redemption requests, all else may vary