2 1 reading 39 portfolio risk and return part i pdf

LOS Case II: When correlation = 0 Portfolio Return = Weighted return of assets LOS Describe the effect on a portfolio’s risk of investing in assets that are less than perfectly correla

LOS

• Portfolio Management – An Overview

• Portfolio Risk and Return – Part I

• Portfolio Risk and Return – Part II

• Basics of Portfolio Planning and Construction

• Risk Management – An Introduction

• Fintech in Investment Management

Portfolio Management

LOS

Major Return Measures

1 Holding Period Return

• The period return (HPR), refers to the change in the value of an

investment over the period it is held, expressed as a percentage of the originally invested amount

• It also captures any additional income that one earns from an

LOS

Example: HPR

• Five years ago, a trader paid $20 per share for 500 shares in an insurance company

• The current share price has grown by 50% of the purchase price

• So far, he has received 12 dividend payments, each amounting to

HPR = (15,000 - 10,000 + 3,000)/10,000 = 80%

HPR = (Ending value – Beginning value + Asset

income)/Beginning value

3 Geometric Mean Return

• The geometric mean return gives the average rate per period on

an investment that is compounded over multiple periods

LOS

4 Money-weighted rate of return

• The money-weighted return accounts for the money invested and

provides the investor with information on the return she earns on her actual investment

• Its calculation is similar to that of the internal rate of return and the

• The nominal rate of return is the amount of money generated by an

investment before factoring in inflation To determine the real rate of return:

𝐑𝐞𝐚𝐥 𝐫𝐚𝐭𝐞 𝐨𝐟 𝐫𝐞𝐭𝐮𝐫𝐧 = 𝟏 + 𝐍𝐨𝐦𝐢𝐧𝐚𝐥 𝐫𝐚𝐭𝐞

𝟏 + 𝐈𝐧𝐟𝐥𝐚𝐭𝐢𝐨𝐧 𝐫𝐚𝐭𝐞

Gross and net return

• Gross return is earned prior to the deduction of fees (management fees, custodial fees, etc.) A net return is the return post-deduction

of fees

LOS Calculate and interpret major return measures and describe their appropriate uses

LOS

A risk-return tradeoff refers to the relationship between risk and

return

• To achieve a higher return, you must accept a higher level of risk

• The following historical returns (1926 – 2008) illustrate as much:

LOS Describe characteristics of the major asset classes that

investors consider in forming portfolios

Asset Class

Average annual nominal return

Risk (Standard deviation

of return)

LOS

Skewness

• Skewness is present when the distribution is not symmetrical

• A distribution with positive skewness has a large number of small

negative values with a few large positive values – the distribution has a long right tail (why most people buy lottery tickets)

• A distribution with negative skewness has a large number of small

positive values with a few large negative values – the distribution has a long left tail (why most people buy insurance)

• Positive skewness: Mode < Median < Mean

Investors like positive skewness because the mean is greater than the median

• Negative skewness: Mean < Median < Mode

LOS Describe characteristics of the major asset classes that

investors consider in forming portfolios

LOS

Kurtosis

• Kurtosis measures the degree to which a distribution is more or less peaked than a normal distribution

Positive kurtosis indicates a relatively peaked distribution

Negative kurtosis indicates a relatively flat distribution

A normal distribution has a kurtosis of 3

• An investment characterized by high kurtosis will have “fat tails”

(higher frequencies of outcomes) at the extreme negative and

positive ends of the distribution curve

• A distribution of returns exhibiting high kurtosis tends to

overestimate the probability of achieving the mean return.

LOS Describe characteristics of the major asset classes that

investors consider in forming portfolios

LOS

Variance of asset returns:

• Measures the volatility/dispersion of returns

• It’s the average squared deviation from the mean

Example:

LOS Calculate and interpret the mean, variance, and covariance (or

correlation) of asset returns based on historical data

Deviation from mean

Square of deviation

𝐓

T = number of periods

• Standard deviation (volatility) is the square root of variance

LOS Calculate and interpret the mean, variance, and covariance (or

correlation) of asset returns based on historical data

LOS

Example:

From the data given, compute the covariance:

LOS Calculate and interpret the mean, variance, and covariance (or correlation) of asset returns based on historical data

Year Return of asset 1Return of asset 2

LOS

Example:

From the information given in the table, calculate the portfolio risk and return

Portfolio return = weighted return of assets

E(Rp) = (0.8 × 9.98%) + (0.2 × 15.8%) = 11.14%

Portfolio variance = 0.82 × 0.172 + 0.22 × 0.32 + 2 × 0.8 × 0.2 × 0.005 =

0.023696

Portfolio risk = Portfolio standard deviation = 0.023696 = 0.1539 = 15.39%

• Should the investor invest in asset 1, asset 2, or both?

 Both: portfolio risk is less than the risk of each respective asset

LOS Calculate and interpret portfolio standard deviation

LOS

How does correlation impact Portfolio Risk?

• Correlation ranges from -1 to +1

 +1 = returns are perfectly positively correlated

 0 = returns of two assets are not correlated

 -1 = returns are perfectly negatively correlated

• What happens to portfolio risk (in a portfolio of two risky assets) when the two assets are perfectly correlated?

 Risk is unaffected; no diversification benefit

• What happens to portfolio risk (in a portfolio of two risky assets) when the two assets are not perfectly correlated?

 Overall portfolio risk is reduced; there is a diversification benefit

A good example will help you understand this >>

LOS Describe the effect on a portfolio’s risk of investing in assets that are less than perfectly correlated

LOS

Case I: When correlation = 1

Portfolio Return = Weighted return of assets

= 0.5 × 20% + 0.5 × 20 = 20%

Portfolio risk

0.52 × 0.32) + (0.52× 0.32) + (2 × 0.5 × 0.5 × 0.3 × 0.3 × 1 = 30%

Comment: Portfolio risk is unaffected; it is simply the weighted average of the

standard deviations of the two assets

LOS Describe the effect on a portfolio’s risk of investing in

assets that are less than perfectly correlated;

LOS

Case II: When correlation = 0

Portfolio Return = Weighted return of assets

LOS Describe the effect on a portfolio’s risk of investing in

assets that are less than perfectly correlated;

LOS

Case III: When correlation = -1

Portfolio Return = Weighted return of assets

= 0.5 × 20% + 0.5 × 20 = 20%

Portfolio risk =

0.52 × 0.32) + (0.52× 0.32) + (2 × 0.5 × 0.5 × 0.3 × 0.3 × −1 = 0%

Comment: Maximum risk reduction occurs with the addition of two assets that

are perfectly negatively correlated

LOS Describe the effect on a portfolio’s risk of investing in

assets that are less than perfectly correlated;

LOS

Risk Aversion refers to individual behavior under uncertainty

• What will you choose? Gamble vs guaranteed outcome?

 Option 1: Guaranteed outcome of $100

 Option 2: Gamble of either $200 or $0? (expected value of $100)

Investor Types

return than a substantial risky investment)

Risk tolerance refers to the amount of risk an investor is willing to take

in order to achieve their investment goals and objectives

• A higher risk tolerance shows a greater willingness to take risk,

implying risk tolerance and risk aversion are negatively correlated

LOS Explain risk aversion and its implications for portfolio

selection

LOS

What’s an Efficient Frontier

Although there are no securities with perfectly negative correlation,

almost all assets are less than perfectly correlated

• Therefore, you can reduce total risk (𝜎p) through diversification If

we consider many assets at various weights, we can generate the

efficient frontier

• The Efficient Frontier represents all the dominant portfolios in

risk/return space

 A portfolio dominates all others if no other equally risky portfolio

has a higher expected return, or if no portfolio with the same expected return has less risk

LOS Describe and interpret the minimum-variance and efficient frontiers of risky assets and the global minimum-variance portfolio

LOS

Example:

• Assume you have the risk/return characteristics of 20 assets

• With the help of the computer, you can calculate all possible portfolio combinations

• The collection of all the minimum variance portfolios would form the

minimum variance frontier

• Along the minimum-variance frontier, the left-most point is a portfolio with minimum variance when compared to all possible portfolios -

the global minimum-variance portfolio

• The Efficient Frontier is the portion of the minimum-variance curve

that lies above and to the right of the global minimum variance

portfolio (Dominance Rule)

LOS Describe and interpret the minimum-variance and efficient frontiers of risky assets and the global minimum-variance portfolio

LOS

Illustration:

LOS Describe and interpret the minimum-variance and efficient frontiers of risky assets and the global minimum-variance portfolio

Global minimum variance portfolio

Efficient frontier consisting

of dominant portfolios

Dominated (inefficient) portfolios Minimum variance frontier

Portfolio standard deviation

LOS

Why the emphasis is on the efficient frontier?

• Portfolios lying on the efficient frontier offer the maximum expected

return for their level of variance of return

• Efficient portfolios use risk efficiently: investors making portfolio

choices in terms of mean return and variance of return can restrict their selections to portfolios lying on the efficient frontier This

simplifies the selection process

• If an investor can quantify his risk tolerance in terms of variance or

SD of return, the efficient portfolio for that level of variance will

represent Optimal-mean variance choice

LOS Describe and interpret the minimum-variance and efficient frontiers of risky assets and the global minimum-variance portfolio

LOS

Utility Theory

• Relative satisfaction from consumption

• Quantification of rankings of choices

• Utility is different for different investors

• Utility can be increased (getting higher return or lower risk),

• Utility can be decreased (increase in risk)

Assumptions

• Investors are risk averse

• Possible to rank order

• Rankings are internally consistent

LOS Explain the selection of an optimal portfolio, given an

investor’s utility (or risk aversion) and the capital allocation line

LOS

What’s an indifferent curve?

• Combination of risk-return pairs acceptable to an investor for a given level of Utility

• All points on a curve have the same utility (investor is indifferent)

• A curve with higher return for a given risk is superior than a curve offering lower returns for the same risk

LOS Explain the selection of an optimal portfolio, given an

investor’s utility (or risk aversion) and the capital allocation line

LOS LOS Explain the selection of an optimal portfolio, given an

investor’s utility (or risk aversion) and the capital allocation line

LOS LOS Explain the selection of an optimal portfolio, given an

investor’s utility (or risk aversion) and the capital allocation line

High risk aversion

Moderate risk aversion

Low risk aversion

LOS LOS Explain the selection of an optimal portfolio, given an

investor’s utility (or risk aversion) and the capital allocation line

Capital Allocation Line (CAL)

• The combination of a risk-free asset and a risky asset (the risky

asset represents multiple portfolios available to the investor)

LOS

To get the optimal portfolio, combine the indifference curves with the

CAL:

LOS Explain the selection of an optimal portfolio, given an

investor’s utility (or risk aversion) and the capital allocation line

LOS

• Portfolio Management – An Overview

• Portfolio Risk and Return – Part I

 Portfolio Risk and Return – Part II

• Basics of Portfolio Planning and Construction

• Risk Management – An Introduction

• Fintech in Investment Management

Portfolio Management