CFA. Risk and Return(Portfolio Management), Study notes of Finance

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Portfolio Risk and Return:

Part I

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INTRODUCTION

• Constructing an optimal portfolio is a crucial goal for investors.
• The process involves evaluating the risk and return of individual assets, creating various portfolios, and

selecting the most efficient ones.

• Key factors considered in portfolio construction are the risk and return of individual assets and the

correlations among them.

• Understanding the investor's risk profile is essential for tailoring the optimal portfolio to their

preferences.

• Different types of investors have varying risk-return preferences.
• The process involves formalizing these preferences using concepts like indifference curves.
• Portfolio risk is a critical aspect, and its calculation and diversification are discussed.
• The reading outlines how to create numerous risky portfolios and narrow down choices to an efficient

set before identifying the optimal one.

• The final step involves combining the chosen risky portfolio with the investor's risk preferences to

determine their optimal portfolio.

• The reading concludes with a summary of the key points and concepts discussed.

Returns ❑ HPR ❑ Arithmetic Mean ❑ Annualized return ❑ Portfolio return ❑ Gross and Net Return ➢ Gross – Return earned by an asset manager ➢ Net – Less the fees and other expenses (actual returns to the investor) ❑ Geometric Mean ❑ Pre-tax and after tax returns ❑ Real returns ❑ Leveraged returns www.proschoolonline.com Copyright©-IMS^ Proschool^ Pvt..Ltd

HISTORICAL RETURN AND RISK

• Historical return and expected return are distinct concepts often confused.
• Historical return refers to past earnings, while expected return is what investors anticipate in the

future.

• Expected return is calculated based on the real risk-free interest rate (rrF), expected inflation (E(π)),

and expected risk premium (E(RP)).

• Expected return is generally positive and is calculated using the formula:

1 + E(R) = (1 + rrF) × [1 + E(π)] × [1 + E(RP)].

• Historical mean return is the actual return earned by an investor from a specific asset in the past.
• Because investments are risky, historical and expected returns are unlikely to be equal for a given time

period.

HISTORICAL RETURN AND RISK

Real Returns of Major US Asset Classes

• Annual inflation rates have fluctuated significantly over the past 92 years, ranging from - 10.30 percent

to +13.31 percent.

• Comparing investment returns across different time periods using nominal returns can be misleading,

so it's better to rely on real returns.

• Real returns on stocks, bonds, and T-bills have been reported since 1900.
• Exhibit 2 illustrates the substantial difference in growth among these asset categories: $1 invested in

stocks grew to $1,654, in bonds to only $10.20, and in T-bills to $2.60 over time.

• Despite the seemingly modest difference in annual real returns (6.5 percent for equities compared to

2.0 percent for bonds), the substantial growth difference arises from compounding over a 118-year

period.

• Exhibit 3 provides real rates of return, with a focus on the geometric mean as a more accurate

representation of returns over multiple holding periods.

• The analysis reveals that real returns for stocks consistently outperform those for bonds.

Nominal Returns and Real Returns A nominal rate of return is the amount of money generated by an investment before factoring in expenses such as taxes, investment fees and inflation. www.proschoolonline.com Copyright©-IMS^ Proschool^ Pvt..Ltd A real rate of return is the annual percentage return realized on an investment, which is adjusted for changes in prices due to inflation or other external effects. This method expresses the nominal rate of return in real terms, which keeps the purchasing power of a given level of capital constant over time. Assume the bank pays interest of 5 % per year on the funds in savings account. If the inflation rate is currently 3 % per year, the real return on your savings is 2 %. In other words, even though the nominal rate of return on savings is 5 %, the real rate of return is only 2 %, which means the real value of your savings only increases by 2 % during a one-year period. Assume your bank pays you interest of 5% per year on the funds in your savings account. If the inflation rate is currently 3% per year, the real return on your savings is 2%. In other words, even though the nominal rate of return on your savings is 5%, the real rate of return is only 2%, which means the real value of your savings only increases by 2% during a one-year period.

Risk of Major Asset Classes

• Exhibit 1 (1926–2017) - Risk for Major Asset Classes in the United States:
• US small company stocks had the highest risk at 31.7 percent.
• US large company stocks followed with a risk of 19.8 percent.
• Long-term government bonds had a risk of 9.9 percent.
• Long-term corporate bonds had a risk of 8.3 percent.
• Treasury bills had the lowest risk at approximately 3.1 percent.
• Exhibit 3 (1900–2017) - Risk for Major Asset Classes Worldwide: 6. World stocks had a risk of 17.

percent.

• World bonds had a risk of 11.0 percent.
• The world excluding the United States had risks of 18.9 percent for stocks and 14.4 percent for bonds.
• Diversification Effect: 9. Diversification is evident when comparing world risk to US risk and world

excluding US risk.

• US stocks had a risk of 20.0 percent, while world excluding US stocks had a risk of 18.9 percent.
• However, when combined, the risk for world stocks was reduced to only 17.4 percent, illustrating the

benefits of diversifying across different regions and asset classes.

Risk–Return Trade-of

Risk Premium :

• The risk premium is the extra

return investors can expect

after adjusting for the risk-

free interest rate.

• Higher-risk investments yield

higher nominal and real risk

premiums.

• Equities outperformed bonds

due to their higher risk,

leading to higher returns for

equity investors.

Cumulative Returns in Real

Terms:

• T-bills had the least volatile

cumulative returns, with an

average real return of 0.

percent per year, adjusted for

inflation.

• Bonds were more volatile

than T-bills but less so than

stocks.

• Stocks, including dividends

and capital gains, had the

highest total return, growing

$1 to $1,654 since 1900, with

an annualized real return of

6.5 percent.

Long-Term Perspective:

• Over extended periods, it

becomes evident that higher

risk is associated with higher

mean returns, supporting the

notion that market prices

reward risk-averse investors

with higher returns over

time.

OTHER INVESTMENT CHARACTERISTICS

Distributional Characteristics

Normal Distribution

Characteristics:

• Mean and median are equal.
• Defined by two parameters: mean and variance.
• Symmetric around the mean.
• 68% of observations within ±1σ of the mean.
• 95% of observations within ±2σ of the mean.
• 99% of observations within ±3σ of the mean.

Inappropriate for

Evaluating Investments:

• Returns are not normally distributed.
• Deviations occur due to skewness (lack of symmetry around the mean).
• Deviations also due to kurtosis or "fat tails" (higher probability of

extreme events).

Skewed Returns: • Returns do not exhibit symmetry around the mean.

Kurtosis or Fat Tails:

• Indicates a higher likelihood of extreme events than a normal

distribution suggests.

OTHER INVESTMENT CHARACTERISTICS

OTHER INVESTMENT CHARACTERISTICS

Kurtosis

• Kurtosis refers to the presence of fat tails or a higher likelihood of extreme returns in a financial

asset.

• It increases the asset's risk beyond what is captured in a mean-variance framework.
• Investors assess kurtosis effects using statistical techniques like value at risk (VaR) and conditional tail

expectations.

• The underestimation of extreme events' probability and magnitude contributed significantly to the

2008 financial crisis.

• Exhibit 5 illustrates the higher likelihood of extreme negative outcomes in stock returns.

Investment Features Market characteristics: refers to effects of liquidity, information availability, firm characteristics, and other external factors that affect the return of an investment. Out of these, Liquidity is one of the most significant factors as it affects the price and bid-ask spread of an investment to a large extent. When two investments have the same expected return, investors prefer the lower risk investment When two investments have the same risk, investors prefer the investment with the higher expected return Risk aversion means investors prefer less risk to more risk Risk Aversion ≠ Minimize Risk. www.proschoolonline.com Copyright©-IMS^ Proschool^ Pvt..Ltd

Concept of Risk Aversion Risk Aversion: Minimize risk for the same amount of return or Maximize return for the same amount of risk. Risk Seeking: Investor chooses to gamble Risk Neutral: investor is indifferent to risk when making an investment decision. He is the middle of the risk spectrum, represented by risk-seeking investors at one end and risk-averse investors at the other Risk Tolerance: willingness of the investor to tolerate risk to achieve and investment goal. isk tolerance is the degree of variability in investment returns that an investor is willing to withstand. www.proschoolonline.com Copyright©-IMS^ Proschool^ Pvt..Ltd