Stock Market Concepts: Distributions, Skewness, and More

We all chase money because
we are afraid to chase
dreams
Andres Ramirez Ph.D.
A few things
On telling it like it is
On team work versus individual work
On your first assignment
What on paper
What on file
What companies are not allowed
On the homework
What stocks not to include
The ones we included
Netflix
Bank of America
JP Morgan
Tesla
Potential Sector Ideas
Fixed Income
Asia (ex China / Japan)
South America
MENAP AFRICA
Commodities
NAFTA Brexit TPP
REITs
TAX reform
Trade war
Crypto-currencies
Your own?
Plan for the day
Company screeners / universe
Teams working on
Policy Statements
Region Sector
Cooking show file
Normality Assumptions
Market returns
Create a Portfolio and calculate returns & Stdev
Market Risk vs stand alone risk
DDM constant growth and super-normal
What we do know about the stock
market
link
On Skew, Kurtosis and other
weird terms
Andres Ramirez, Ph.D.
Return Distributions
Return Distributions cont.
Right Skew
Skew >0 
 Right / Positive
Skew = 0 
 symmetrical
Skew < 0 
 Left / Negative
Return Distributions cont.
Kurt>3 
 Leptokurtic
Kurt=3 
 Mesokurtic
Kurt < 3 
 Platykurtic
Do you believe in Magic?
 
 
 
Returns Distribution for Two Perfectly Negatively
Correlated Stocks (
ρ
 = -1.0)
8-13
Returns Distribution for Two Perfectly Positively
Correlated Stocks (
ρ
 = 1.0)
8-14
Partial Correlation, 
ρ
 = +0.35
8-15
Creating a Portfolio:  Beginning with One Stock and
Adding Randomly Selected Stocks to Portfolio
σ
p
 decreases as stocks added, because they
would not be perfectly correlated with the
existing portfolio.
Expected return of the portfolio would
remain relatively constant.
Eventually the diversification benefits of
adding more stocks dissipates (after about 10
stocks), and for large stock portfolios, 
σ
p
tends to converge to 
 20%.
8-16
Illustrating Diversification Effects of a Stock
Portfolio
8-17
Breaking Down Sources of Risk
Stand-alone risk = Market risk + Diversifiable risk
Market risk – portion of a security’s stand-
alone risk that cannot be eliminated through
diversification.  Measured by beta.
Diversifiable risk – portion of  a security’s
stand-alone risk that can be eliminated
through proper diversification.
8-18
Failure to Diversify
 
If an investor chooses to hold a one-stock
portfolio (doesn’t diversify), would the investor
be compensated for the extra risk they bear?
NO!
Stand-alone risk is not important to a well-diversified
investor.
Rational, risk-averse investors are concerned with 
σ
p
, which
is based upon market risk.
There can be only one price (the market return) for a given
security.
No compensation should be earned for holding
unnecessary, diversifiable risk.
8-19
Capital Asset Pricing Model (CAPM)
Model linking risk and required returns.
CAPM suggests that there is a Security
Market Line (SML) that states that a stock’s
required return equals the risk-free return
plus a risk premium that reflects the stock’s
risk after diversification.
r
i
 = r
RF 
+ (r
M 
– r
RF
)b
i
Primary conclusion: The relevant riskiness of
a stock is its contribution to the riskiness of a
well-diversified portfolio.
8-20
Beta
Measures a stock’s market risk, and shows a
stock’s volatility relative to the market.
Indicates how risky a stock is if the stock is
held in a well-diversified portfolio.
Comments on Beta
If beta = 1.0, the security is just as risky as the
average stock.
If beta > 1.0, the security is riskier than
average.
If beta < 1.0, the security is less risky than
average.
Most stocks have betas in the range of 0.5 to
1.5.
Can the beta of a security be negative?
 
Yes, if the correlation between Stock i and the
market is negative (i.e., 
ρ
i,m
 < 0).
If the correlation is negative, the regression
line would slope downward, and the beta
would be negative.
However, a negative beta is highly unlikely.
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Explore key concepts in the stock market such as return distributions, skewness, kurtosis, and correlation between stocks. Gain insights into potential sector ideas and market risks for informed investing decisions.

  • Stock Market
  • Distributions
  • Skewness
  • Investing
  • Sector Ideas

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  1. We all chase money because we are afraid to chase dreams Andres Ramirez Ph.D.

  2. A few things On telling it like it is On team work versus individual work On your first assignment What on paper What on file What companies are not allowed On the homework

  3. What stocks not to include The ones we included Netflix Bank of America JP Morgan Tesla

  4. Potential Sector Ideas Fixed Income Asia (ex China / Japan) South America MENAP AFRICA Commodities NAFTA Brexit TPP REITs TAX reform Trade war Crypto-currencies Your own?

  5. Plan for the day Company screeners / universe Teams working on Policy Statements Region Sector Cooking show file Normality Assumptions Market returns Create a Portfolio and calculate returns & Stdev Market Risk vs stand alone risk DDM constant growth and super-normal

  6. What we do know about the stock market link

  7. On Skew, Kurtosis and other weird terms Andres Ramirez, Ph.D.

  8. Return Distributions

  9. Return Distributions cont. Skew >0 Right / Positive Skew = 0 symmetrical Skew < 0 Left / Negative Right Skew

  10. Return Distributions cont. Kurt>3 Leptokurtic Kurt=3 Mesokurtic Kurt < 3 Platykurtic

  11. Do you believe in Magic?

  12. Returns Distribution for Two Perfectly Negatively Correlated Stocks ( = -1.0) 8-13

  13. Returns Distribution for Two Perfectly Positively Correlated Stocks ( = 1.0) Stock M Portfolio MM Stock M 25 25 25 15 15 15 0 0 0 -10 -10 -10 8-14

  14. Partial Correlation, = +0.35 8-15

  15. Creating a Portfolio: Beginning with One Stock and Adding Randomly Selected Stocks to Portfolio p decreases as stocks added, because they would not be perfectly correlated with the existing portfolio. Expected return of the portfolio would remain relatively constant. Eventually the diversification benefits of adding more stocks dissipates (after about 10 stocks), and for large stock portfolios, p tends to converge to 20%. 8-16

  16. Illustrating Diversification Effects of a Stock Portfolio 8-17

  17. Breaking Down Sources of Risk Stand-alone risk = Market risk + Diversifiable risk Market risk portion of a security s stand- alone risk that cannot be eliminated through diversification. Measured by beta. Diversifiable risk portion of a security s stand-alone risk that can be eliminated through proper diversification. 8-18

  18. Failure to Diversify If an investor chooses to hold a one-stock portfolio (doesn t diversify), would the investor be compensated for the extra risk they bear? NO! Stand-alone risk is not important to a well-diversified investor. Rational, risk-averse investors are concerned with p, which is based upon market risk. There can be only one price (the market return) for a given security. No compensation should be earned for holding unnecessary, diversifiable risk. 8-19

  19. Capital Asset Pricing Model (CAPM) Model linking risk and required returns. CAPM suggests that there is a Security Market Line (SML) that states that a stock s required return equals the risk-free return plus a risk premium that reflects the stock s risk after diversification. ri = rRF + (rM rRF)bi Primary conclusion: The relevant riskiness of a stock is its contribution to the riskiness of a well-diversified portfolio. 8-20

  20. Beta Measures a stock s market risk, and shows a stock s volatility relative to the market. Indicates how risky a stock is if the stock is held in a well-diversified portfolio.

  21. Comments on Beta If beta = 1.0, the security is just as risky as the average stock. If beta > 1.0, the security is riskier than average. If beta < 1.0, the security is less risky than average. Most stocks have betas in the range of 0.5 to 1.5.

  22. Can the beta of a security be negative? Yes, if the correlation between Stock i and the market is negative (i.e., i,m < 0). If the correlation is negative, the regression line would slope downward, and the beta would be negative. However, a negative beta is highly unlikely.

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