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AFM 273 > chp 11 > Flashcards

chp 11 Flashcards

1
Q

define portfolio weights

A

the fraction of the total investment in a portfolio held in each individual investment in the portfolio

xi = value of investment i/ total value of portfolio

portfolio weights add up to 1

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2
Q

what’s the expected return of a portfolio

A

the weighted average of the expected returns of the investments within it, using the portfolio weights

E[Rp] = E * [sum of xiRi] = sum of E[xiRi] = sum fo xi*E[Ri]

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3
Q

what happens when stocks are combined into a portfolio

A

combining stocks in a portfolio eliminates some of their risk through diversification. The amount of risk that will remain depends on the degree to which the stocks are exposed to common risks

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4
Q

phenomena of diverisification

A

First, by combining stocks into a portfolio, we reduce risk through diversification. Because the prices of the stocks do not move identically, some of the risk is averaged out in a portfolio. As a result, both portfolios have lower risk than the individual stocks. Second, the amount of risk that is eliminated in a portfolio depends on the degree to which the stocks face common risks and their prices move together. Because the two airline stocks tend to perform well or poorly at the same time, the portfolio of airline stocks has a volatility that is only slightly lower than that of the individual stocks. The airline and oil stocks, by contrast, do not move together; indeed, they tend to move in opposite directions. As a result, additional risk is cancelled out, making that portfolio much less risky. Again, this benefit of diversification is obtained without any reduction in the average return.

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5
Q

define Covariance

A

the expected product of the deviation of each return from its mean

cov between returns Ri and Rj
Cov(Ri, Rj) = E[(Ri])(Rj - E[Rj])]

estimate of the covariance from historical data:
Cov(Ri, Rj) = (1/(T-1))sum of (Ri, t - averageRi)(Rj, t = averageRj)

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6
Q

define correlation

A

the covariance of the returns divided by the standard deviation of each return; a measure of the common risk shared by stocks that doesn’t depend on their volatility

Corr(Ri, Rj) = Cov(Ri, Rj) / [SD(Ri)*SD(RJ)] = Var(Rs)/SD(Rs)^2 = 1?

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7
Q

why is it difficult to interpret the magnitude of covariance

A

While the sign of the covariance is easy to interpret, its magnitude is not. It will be larger if the stocks are more volatile (and so have larger deviations from their expected returns), and it will be larger the more closely the stocks move in relation to each other. In order to control for the volatility of each stock, and quantify the strength of the relationship between them, we can calculate the correlation between two stock return

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8
Q

what does it mean if the correlation is close to +1, 0, or -1

A

The closer the correlation is to , the more two stocks’ returns tend to move as a result of a common risk. When the correlation (and thus the covariance) equals 0, the returns are uncorrelated; that is, they have no tendency to move either together or in opposition to one another. Independent risks are uncorrelated. Finally, the closer the correlation is to , the more the two stocks’ returns tend to move in opposite directions.

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9
Q

what’s the formula of a two-stock portfolio with expected return

A

Rp = x1R1 + x2R2

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10
Q

what’s the variance of a two-stock porftolio

A

Var(Rp) = Cov(Rp, Rp)
= Cov(x1R1 + x2R2, x1R1 + x2R2)
= x1x1Cov(R1, R1) + x1x2cov(R1, R2) + x2x1Cov(R2, R1)

and with CovRi, Ri) = Vae(Ri)

Var(Rp) = x21Var(r1) + x22Var(r2) + 2x1x2Cov(R1, R2)

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11
Q

what’s volatility

A

square root fo variance

Sd(Rp) = square root (Var(Rp))

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12
Q

what does the variance of a portfolio equal to

A

equal to the weighted average covariance of each stock with the portfolio. This expression reveals that the risk of a portfolio depends on how each stock’s return moves in relation to it.

or equal to the sum of the covariances of the returns of all pairs of stocks in the portfolio multiplied by each of their portfolio weights.117 That is, the overall variability of the portfolio depends on the total co-movement of the stocks within it

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13
Q

define an equally weighted porfolio

A

a portfolio in which the same dollar amount is invested in each stock

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14
Q

what’s the variance of an equally weighted portfolio of n stocks formula

A

Var(Rp) = 1/n (average variance of the individual stocks) + (1- (1/n)) (average covariance between the stocks)

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15
Q

what’s the formula for portfolio with arbitrary weights - correlation and sd = ?

A

check textbook

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16
Q

define an inefficicient portfolio

A

describes a portfolio for which it’s possible to find another portfolio that has higher expected return and lower volatility

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17
Q

does correlation have an effect on expected return of a porfolio

A

no

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18
Q

what happens tot eh portfolio curve as correlation and volatility lowers?

A

will bend to teh let to a greater degree

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19
Q

what happens when correlation is 1, less than 1 or negative?

A

When the stocks are perfectly positively correlated, the set of portfolios is identified by the straight line between them. In this extreme case (the red line in Figure 11.4), the volatility of the portfolio is equal to the weighted average volatility of the two stocks—there is no diversification. When the correlation is less than 1, however, the volatility of the portfolios is reduced due to diversification, and the curve bends to the left. The reduction in risk (and the bending of the curve) becomes greater as the correlation decreases. At the other extreme of perfect negative correlation (the blue line), the line again becomes straight, this time reflecting off the vertical axis. In particular, when the two stocks are perfectly negatively correlated, it becomes possible to hold a portfolio that bears absolutely no risk.

20
Q

define long position

A

positive investment in a security

21
Q

define short position

A

a negative investment in a security created by engaging in a short sale

22
Q

define short sale

A

a transaction in which you sell a stock that you do not own and then buy that stock back in the future.

23
Q

define efficient frontier

A

the set of portfolios that can be formed from a given set of investments with the property that each portfolio has the highest possible expected return that can be attained without increasing its volatility

24
Q

what does adding a new investment lead to

A

allows for greater diversification and improves the efficient frontier.

Even though the added stocks generally offer inferior risk–return combinations on their own, because they allow for additional diversification, the efficient frontier improves with their inclusion. Thus, to arrive at the best possible set of risk and return opportunities, we should keep adding stocks until all investment opportunities are represented. Ultimately, based on our estimates of returns, volatilities, and correlations, we can construct the efficient frontier for all available risky investments showing the best possible risk and return combinations that can be obtained by optimal diversification.

25
Q

define buying stocjs on a margin

A

Borrowing money to invest in stocks

26
Q

define sharpe ratio

A

a portfolio’s excess return divided by its volatility used to measure the ratio of reward to volatility provided by a portfolio

= portfolio excess return/ portfolio volatility = (E[Rp] - rf) / SD(Rp)

The Sharpe ratio measures the ratio of reward-to-volatility provided by a portfolio.123 The optimal portfolio to combine with the risk-free asset will be the one with the highest Sharpe ratio, where the line with the risk-free investment just touches, and so is tangent to, the efficient frontier of risky investments,

27
Q

define tangent portfolio

A

a portfolio with the highest sharpe ratio; the point of tangency to the efficient frontier of a line drawn from the risk free asset; the market portfolio if the CAPM holds

Because the tangent portfolio has the highest Sharpe ratio of any portfolio in the economy, the tangent portfolio provides the biggest reward per unit of volatility of any portfolio available

28
Q

what’s the optimal portfolio

A

very investor should invest in the tangent portfolio independent of his or her taste for risk. The investor’s preferences will determine only how much to invest in the tangent portfolio versus the risk-free investment. Conservative investors will invest a small amount, choosing a portfolio on the line near the risk-free investment. Aggressive investors will invest more, choosing a portfolio that is near the tangent portfolio or even beyond it by buying stocks on margin. Both types of investors will choose to hold the same portfolio of risky assets, the tangent portfolio.

29
Q

what are efficient portfolios when considering risk-free and tangent portfolio

A

all efficient portfolios are combinations of the risk-free investment and the tangent portfolio.

The efficient portfolio is the tangent portfolio, the portfolio with the highest Sharpe ratio in the economy. By combining it with the risk-free investment, an investor will earn the highest possible expected return for any level of volatility he or she is willing to bear.

30
Q

what are the consequences of selling some risk free assets or borrowing money and investing the proceeds in an investment

A

Expected return: Because we are giving up the risk-free return and replacing it with i’s return, our expected return will increase by i’s excess return, E[Ri] - rf

2.Volatility: We will add the risk that i has in common with our portfolio (the rest of i’s risk will be diversified

31
Q

what’s the relationship between the beta and portfolio

A

beta measures the sensitivity of the investment i to the fluctuations of the portfolio P. That is, for each 1% change in the portfolio’s excess return, the investment’s excess return is expected to change by percent due to risks that i has in common with P.

increasing the amount invested in i will increase the Sharpe ratio of portfolio P if its expected return E[Ri] exceeds the required return given portfolio P

32
Q

defined required return

A

expected return that is necessary to compensate for the risk investment i will contribute to the portfolio. The required return for an investment i is equal to the risk-free interest rate plus a risk premium that is equal to the risk premium of the investor’s current portfolio, P, scaled by i’s sensitivity to P, . If i’s expected return exceeds this required return, then adding more of it will improve the performance of the portfolio.

33
Q

when is a portfolio considered efficient?

A

A portfolio is efficient if and only if the expected return of every available security equals its required return.

34
Q

what are the 3 main assumptions that underlie CAPM

A
  1. Investors can buy and sell all securities at competitive market prices (without incurring taxes or transactions costs) and can borrow and lend at the risk-free interest rate.
  2. Investors hold only efficient portfolios of traded securities—portfolios that yield the maximum expected return for a given level of volatility.
  3. Investors have homogeneous expectations regarding the volatilities, correlations, and expected returns of securities.
35
Q

define homogenous expectations

A

a theoretical situation in which all investors have the same estimates concerning future investment returns

36
Q

what is the efficient tangent portfolio of risky securities

A

must equal to the market portfolio

37
Q

define market portfolio

A

portfolio of all risky securities available in the market

38
Q

why is the market portfolio deemed as efficient

A

The insight that the market portfolio is efficient is really just the statement that demand must equal supply. All investors demand the efficient portfolio, and the supply of securities is the market portfolio; hence the two must coincide. If a security was not part of the efficient portfolio, then no investor would want to own it, and demand for this security would not equal its supply. This security’s price would fall, causing its expected return to rise until it became an attractive investment. In this way, prices in the market will adjust so that the efficient portfolio and the market portfolio coincide, and demand equals supply.

39
Q

define the capital market line (CML)

A

when plotting expected returns versus volatility, the line from the risk free investment throuhg the efficient portfolio of risky stocks (the portfolio that has hte highest possible Sharpe ratio),

in CAPM, it’s the line from the risk-free investment through the market portfolio. shows the highest possible expected return that can be obtained for any given volatility

according to CAPM, all investors should choose a portfolio on the capital market line by holding some combination of the risk free security and the market portfolio

40
Q

what’s the formula for the CAPM equation for the expected return

A

check the textbook

41
Q

how to find the appropriate risk premium

A

rescale the market risk premium (the amount by which the market’s expected return exceeds the risk-free rate) by the amount of market risk present in the security’s returns, measured by its beta with the market.

The beta of a security measures its volatility due to market risk relative to the market as a whole, and thus captures the security’s sensitivity to market risk.

42
Q

how to interpret the CAPM equation

A

Following the Law of One Price, in a competitive market, investments with similar risk should have the same expected return. Because investors can eliminate firm-specific risk by diversifying their portfolios, the right measure of risk is the investment’s beta with the market portfolio, . As the next example demonstrates, the CAPM Eq. 11.22states that the investment’s expected return should therefore match the expected return of the capital market line portfolio with the same level of market risk.

43
Q

define the security market line

A

the pricing implication of the CAPM, it specifies a linear relation between the risk premium of a security and its beta with the market portfolio

is the line along which all individual securities should lie when plotted according to their expected return and beta, as shown in panel

44
Q

what’s the distance of each stock to the right of the capital market line

A

due to its diversifiable risk

45
Q

what’s the beta of a portfolio

A

the weighted average beta of the securities in the portfolio

45
Q

what are the 2 major conclusions of CAPM

A

The market portfolio is the efficient portfolio. Therefore, the highest expected return for any given level of volatility is obtained by a portfolio on the capital market line, which combines the market portfolio with risk-free saving or borrowing.

The risk premium for any investment is proportional to its beta with the market. Therefore, the relationship between risk and the required return is given by the security market line

The CAPM model is based on strong assumptions. Because some of these assumptions do not fully describe investors’ behaviour, some of the model’s conclusions are not completely accurate; it is certainly not the case that every investor holds the market portfolio

46
Q
A

AFM 273 (12 decks)

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