CHAPTER 13: Return, risk, and the
security market line
Important lesson from capital market history:
 There is a reward, on average, for bearing risk, which is called risk premium
 This risk premium is larger for riskier investments
2 types of risk:
 Systematic risk affects almost all assets in the economy, at least to some degree
 Unsystematic risk affects at most a small number of assets
 highly diversified portfolios will tend to have almost no unsystematic risk
To a diversified investor, only systematic risk matters
Security market line (SML): famous relationship between risk and return
“Beta” coefficient: one of the centerpieces of modern finance
I.
Key concepts
Expected returns and variances
Return: total gain or loss experienced on an investment over a given period (per year)
𝑹𝒕 =
𝑪𝒕 + 𝑷𝒕 − 𝑷𝒕−𝟏
𝑷𝒕−𝟏
Expected return: the return on a risky asset expected in the future
𝒏
𝑬𝒙𝒑𝒆𝒄𝒕𝒆𝒅 𝒓𝒆𝒕𝒖𝒓𝒏 = 𝝁 = 𝑬(𝑹) = ∑ 𝑹𝒊 × 𝑷𝒊
𝒊=𝟏
𝑷𝒓𝒐𝒋𝒆𝒄𝒕𝒆𝒅 (𝑬𝒙𝒑𝒆𝒄𝒕𝒆𝒅)𝒓𝒊𝒔𝒌 𝒑𝒓𝒆𝒎𝒊𝒖𝒎 = 𝑬𝒙𝒑𝒆𝒄𝒕𝒆𝒅 𝒓𝒆𝒕𝒖𝒓𝒏 − 𝑹𝒊𝒔𝒌 𝒇𝒓𝒆𝒆 𝒓𝒂𝒕𝒆
Required rate of return: return on an investment required by an investor given market interest rates and
the investment’s risk
𝑹𝒆𝒒𝒖𝒊𝒓𝒆𝒅 𝒓𝒂𝒕𝒆 𝒐𝒇 𝒓𝒆𝒕𝒖𝒓𝒏
= 𝑹𝒊𝒔𝒌 𝒇𝒓𝒆𝒆 𝒓𝒂𝒕𝒆 𝒐𝒇 𝒓𝒆𝒕𝒖𝒓𝒏 + 𝑹𝒊𝒔𝒌 𝒑𝒓𝒆𝒎𝒊𝒖𝒎 (𝑵𝒐𝒏𝒅𝒊𝒗𝒆𝒓𝒔𝒊𝒇𝒊𝒂𝒃𝒍𝒆 𝒓𝒊𝒔𝒌)
𝒏
𝟐
𝑽𝒂𝒓(𝑹) = 𝝈 = ∑[𝑹𝒊 − 𝑬(𝑹)]𝟐 × 𝑷𝒊
𝒊=𝟏
𝑫(𝑹) = 𝝈 = √𝑽𝒂𝒓 (≈ 50%low number): higher SD, higher risk
II.
Portfolios
Portfolios: combining several securities in a portfolio can actually reduce overall risk; a group of assets
such as stocks and bonds held by an investor
Portfolio weight: percentage of a portfolio’s total value that is in a particular asset
𝑨 𝒑𝒂𝒓𝒕𝒊𝒄𝒖𝒍𝒂𝒓 𝒂𝒔𝒔𝒆𝒕
𝑷𝒐𝒓𝒕𝒇𝒐𝒍𝒊𝒐 𝒘𝒆𝒊𝒈𝒉𝒕 =
𝑻𝒐𝒕𝒂𝒍 𝒑𝒐𝒓𝒕𝒇𝒐𝒍𝒊𝒐 𝒗𝒂𝒍𝒖𝒆
ALL ABOUT CORRELATION
𝒏
𝑬(𝑹𝒑 ) = ∑ 𝒘𝒊 × 𝑬(𝑹𝒊 )
𝒊=𝟏
E(Rp) is between E(Ri1) and E(Ri2)
𝑽𝒂𝒓𝒊𝒂𝒏𝒄𝒆 = 𝝈𝟐𝑷 = 𝒘𝟐𝑨 𝝈𝟐𝑨 + 𝒘𝟐𝑨 𝝈𝟐𝑨 + 𝟐𝒘𝑨 𝒘𝑩 𝝆𝑨𝑩 𝝈𝑨 𝝈𝑩
III.
Announcements, surprises, and expected returns
𝑻𝒐𝒕𝒂𝒍 𝒓𝒆𝒕𝒖𝒓𝒏 (𝑹) = 𝑬(𝑹) + 𝑼𝒏𝒆𝒙𝒑𝒆𝒄𝒕𝒆𝒅 𝒓𝒆𝒕𝒖𝒓𝒏 (𝑼) (positive or negative but through time, =0)
On average, the actual return = expected return
A common way of saying an announcement isn’t news is to say that the market has already “discounted”
the announcement
Innovation (surprise): difference between actual result and the forecast
News about the future is what matters
𝑨𝒏𝒏𝒐𝒖𝒏𝒄𝒆𝒎𝒆𝒏𝒕 = 𝑨𝒏𝒕𝒊𝒄𝒊𝒑𝒂𝒕𝒆𝒅 (𝑬𝒙𝒑𝒆𝒄𝒕𝒆𝒅)𝒑𝒂𝒓𝒕 + 𝑺𝒖𝒓𝒑𝒓𝒊𝒔𝒆 = 𝑬(𝑹) + 𝑼
IV.
Risk: systematic and unsystematic
Investment risk: related to the probability of earning a low or negative actual return
 Stand-along risk
 Portfolio risk
Investing in more than 1 security to reduce risk
Risk-free: if we always receive exactly what we expect, then the investment is perfectly predictable
Systematic risk (market risk): a risk that influences a large number of assets
Unexpected changes in interest rates; in cash flows due to tax rate changes, foreign competition,
and the overall business cycle; covid; war
Unsystematic risk (unique or asset-specific risk): a risk that affects at most a small number of assets
Company’s labor force goes on strike; company’s top management dies in a plane crash; huge oil
tank bursts and floods a company’s production area
𝑹 = 𝑬(𝑹) + 𝑺𝒚𝒔𝒕𝒆𝒎𝒂𝒕𝒊𝒄 𝒑𝒐𝒓𝒕𝒊𝒐𝒏 (𝒎) + 𝑼𝒏𝒔𝒚𝒔𝒕𝒆𝒎𝒂𝒕𝒊𝒄 𝒑𝒐𝒓𝒕𝒊𝒐𝒏 (𝝐)
V.
Diversification and portfolio risk
Principle of diversification: spreading an investment across a number of assets will eliminate some, but
not all, of the risk
Diversification: process of spreading investment across assets (thereby forming a portfolio)


Diversifiable risk: some of riskiness associated with individual assets can be eliminated by
forming portfolios
Nondiversifiable risk: a minimum level of risk that cannot be eliminated simply by diversifying
Diversification reduces exposure to extreme outcomes, both good and bad
Unsystematic risk (often used as diversifiable risk interchangeably) is essentially eliminated by
diversification, so a portfolio with many assets has almost no unsystematic risk
Systematic risk and nondiversifiable risk are used interchangeably
𝑻𝒐𝒕𝒂𝒍 𝒓𝒊𝒔𝒌 = 𝑺𝒚𝒔𝒕𝒆𝒎𝒂𝒕𝒊𝒄 𝒓𝒊𝒔𝒌 + 𝑼𝒏𝒔𝒚𝒔𝒕𝒆𝒎𝒂𝒕𝒊𝒄 𝒓𝒊𝒔𝒌
For a well-diversified portfolio, unsystematic risk is negligible; essentially all of the risk is systematic
VI.
Systematic risk and beta
Systematic risk principle: expected return on a risky asset depends only on that asset’s systematic risk
Market does not reward risks that are borne unnecessarily
No matter how much total risk an asset has, only the systematic portion is relevant in determining
the expected return (and the risk premium) on that asset
Beta coefficient (β): amount of systematic risk present in a particular risky asset relative to that in an
average risky asset; measure of how an individual stock’s returns vary with market returns; measure of
the sensitivity of an individual stock’s returns to changes in the market
Expected return, and thus the risk premium, of an asset depends only on its systematic risk
Assets with larger β  greater systematic risks  greater expected returns
Not all betas are created equal
∑ 𝑨𝒔𝒔𝒆𝒕′ 𝒔 𝒃𝒆𝒕𝒂
𝑷𝒐𝒓𝒕𝒇𝒐𝒍𝒊𝒐 𝒘𝒆𝒊𝒈𝒉𝒕
β=1: average market risk  stock is no more or less volatile than the market
β>1: more volatile than market (ex: technology firms)
β<1: less volatile than market (ex: utilities)
𝑷𝒐𝒓𝒕𝒇𝒐𝒍𝒊𝒐 𝒃𝒆𝒕𝒂 =



How to calculate beta
1. run a regression line of past returns on stock i versus returns on the market
2. the regression line is called the characteristic line
𝑹𝒊 = 𝜶 + 𝜷𝑹𝑴
3. the slope coefficient of the characteristic line is defined as the beta coefficient
∑(𝒚 − 𝒚
̅)(𝒙 − 𝒙
̅)
𝜷=
∑(𝒙 − ̅
𝒙)𝟐
̅ − 𝜷𝒙
̅
𝜶=𝒚
VII. The security market line
Security market line (SML): also known as Capital asset pricing model (CAPM), gives the risk/return
relationship for individual stocks
Measure of risk used in SML is β
𝑬(𝑹𝒊 ) = 𝑹𝒇 + [𝑬(𝑹𝑴 ) − 𝑹𝒇 ] × 𝜷𝒊
Rf: Return for bearing no market risk
E(RM): Portfolio’s exposure to market risk
βi: Reward for bearing market risk