Section 3.5 - Margin Call
Margin Ratio =
𝑀𝑎𝑟𝑘𝑒𝑡 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑆𝑒𝑐𝑢𝑟𝑖𝑡𝑦−𝐴𝑚𝑜𝑢𝑛𝑡 𝐵𝑜𝑟𝑟𝑜𝑤𝑒𝑑
𝑀𝑎𝑟𝑘𝑒𝑡 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑆𝑒𝑐𝑢𝑟𝑖𝑡𝑦
=
𝐸𝑞𝑢𝑖𝑡𝑦 𝑉𝑎𝑙𝑢𝑒
𝑀𝑎𝑟𝑘𝑒𝑡 𝑉𝑎𝑙𝑢𝑒
To find the minimum price which satisfies the margin solve for P:
𝐴𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑆𝑡𝑜𝑐𝑘 ℎ𝑒𝑙𝑑 ∗ 𝑃 − 𝐴𝑚𝑜𝑢𝑛𝑡 𝑏𝑜𝑟𝑟𝑜𝑤𝑒𝑑
𝐴𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑆𝑡𝑜𝑐𝑘 ℎ𝑒𝑙𝑑 ∗ 𝑃
= 𝑀𝑖𝑛𝑖𝑚𝑢𝑚 𝑚𝑎𝑟𝑔𝑖𝑛 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑚𝑒𝑛𝑡
Margin Ratio on a Short Sell =
𝑀𝑎𝑟𝑘𝑒𝑡 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐴𝑙𝑙 𝐴𝑠𝑠𝑒𝑡𝑠
𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑆𝑡𝑜𝑐𝑘
To find the minimum price which satisfies the margin solve for P:
𝑀𝑎𝑟𝑘𝑒𝑡 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑎𝑙𝑙 𝐴𝑠𝑠𝑒𝑡𝑠
𝐴𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑆𝑡𝑜𝑐𝑘 ℎ𝑒𝑙𝑑 ∗ 𝑃
= 1 + 𝑀𝑖𝑛𝑖𝑚𝑢𝑚 𝑚𝑎𝑟𝑔𝑖𝑛 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑚𝑒𝑛𝑡
Section 3.6 - Regulations of Securities Markets
Most trading legislation in Canada is done at a provincial level
The Securities Exchange Committee (SEC) is the largest legislative body overseeing trading.
In response to scandals in 2000-2002 the United States implemented the Sarbanes-Oxley act which has been highly controversial as businesses find it extremely expensive to satisfy.
Meanwhile in Canada we implemented three sets of rules: a) CEO/CFO certification of quarterly and annual reports b) Companies must have fully independent and financially literate auditors c) Companies must perform tests on their accounting procedures which the auditors need to examine and give an opinion on to investors
Much of the securities industry relies on self-regulation
Summary: Securities trading is regulated by the provincial securities commission and by selfregulation of the exchanges and the dealer associations. Many of the important regulations have to do with full disclosure of relevant information concerning the securities in question.
Insider trading rules prohibit traders from attempting to profit from inside information.
Key Terms:
 Circuit Breakers: market pausing devices put in place by U.S regulatory organizations in order to reduce the risk of extreme volatilities in the markets and to give investors time to assess these swings if they occur.
 Canada Business Corporations Act: governs the conduct of business firms

 Ontario Companies Act: provincial legislation established in 1907. Ontario Securities Act is the first provisional securities act, founded in 1945
 Canadian Investor Protection Fund (CIPF): Assures bank account holders that if their bank goes bankrupt they will recover their savings up to $1 million
 Securities Exchange Act: established in 1934 to ensure the full disclosure of relevant information relating to the issue of new securities and periodic release of financial information for secondary trading. Securities Exchange Commission (SEC) regulates securities exchanges, OTC trading, brokers and dealers.
 Self-Regulatory Organizations (SROs): comprises of various exchanges and the Investment
Dealers Association (IDA) representing member firms. Canadian Securities Institute (CSI) serves the SROs by providing educational services to industry members.
Section 4.6 – The Normal Distribution
Standard Deviation: a value calculated to indicate the extent of deviation for a group.
Skew: a measure of a distribution’s asymmetry. In a positive skew, the standard deviation overestimates risk. Conversely when a distribution is negatively skewed it underestimates risk.
𝑆𝑘𝑒𝑤 =
𝐸[𝑟(𝑠) − 𝐸(𝑟)]
3 𝜎 3
Kurtosis: is a measure of the degree of fat tails. When fatter tails are present the standard deviation will underestimate the likelihood of extreme events.
𝐸[𝑟(𝑠) − 𝐸(𝑟)] 4 𝜎 4
− 3
Section 4.7 – Historical Market Returns (No Notes)

Section 5.1 Risk and Risk Averse
𝑈 = 𝐸(𝑟) – .005𝐴𝜎 2
Section 5.4 – Portfolios of One Risky Asset and One Risk-Free Asset
Expected Return of Complete Portfolio = Risk Free Rate + Proportion of investment budget allocated to risky asset * Risk Premium
𝐸(𝑟 𝑐
) = 𝑅 𝑓
+ 𝑦(𝐸(𝑟 𝑝
) − 𝑅 𝑓
)
Standard Deviation of Complete Portfolio = Proportion invested in risky asset * standard deviation of risk asset 𝜎 𝑐
= 𝑦 ∗ (𝜎 𝑝
)
Capital Allocation Line (CAL): A line representing all possible combinations of risky and risk-free assets.
Also known as the "reward-to-variability ratio"
Slope of the CAL = Risk Premium/ Standard Deviation of Risky Asset
𝐸(𝑟 𝑝
) − 𝑅 𝑓 𝜎 𝑝
Section 6.1 – Diversification and Portfolio Risk
Market Risk/Systemic Risk/Non-diversifiable Risk: Risk associated with the general markets and which are cannot be eliminated through diversification.
Unique Risk/Firm-Specific Risk/Non-systematic Risk/Diversifiable Risk: Risk associated with specific securities and which can be eliminated through diversification.
Section 6.2 – Portfolios of Two Risky Assets
Covariance =

S

B
Expected Return on Portfolio = Weight of X * Expected Return of X + Weight of Y * Expected Return of Y
𝐸(𝑟 𝑝
) = 𝑤
𝐷
𝐸(𝑟
𝐷
) + 𝑤
𝐸
𝐸(𝑟
𝐸
)
Variance of Portfolio = Weight of X * Variance of X + Weight of Y * Variance of Y + 2 * Weight X * Weight
Y * Covariance of X and Y 𝜎 2 𝑝
= 𝑤
2
𝐸 𝜎
2
𝐷
+ 𝑤
2
𝐸 𝜎
2
𝐸
+ 2𝑤
𝐷 𝑤
𝐸
𝐶𝑂𝑉( 𝑟𝑑,𝑟𝑒
)
To Minimize the Standard Deviation

1) Find the weight D: 𝜎
2
𝐸 𝜎
2
𝐸
−𝐶𝑜𝑣
(𝑟𝑑,𝑟𝑒)
+𝜎
2
𝐷
−2𝐶𝑂𝑉
(𝑟𝑑,𝑟𝑒)
2) Find Weight E: 1 – Weight D
3) Plug in weights into portfolio variance formula
Summary: Although the expected rate of return of any portfolio is simply the weighted average of the asset expected return, this is not true of the portfolio’s standard deviation. Potential benefits from diversification arise when correlation is less than perfectly positive. The lower the correlation coefficient, the greater the potential benefit of diversification. In the extreme case of perfect negative correlation, we have a perfect hedging opportunity and can construct a zero-variance portfolio.
Section 6.3 – Asset Allocation with Stocks, Bonds, and T-Bills
The Capital Allocation Line which lies tangent on the opportunity set yields the optimal risky portfolio
Utilizing both the lessons learned from investing in a portfolio with a risky asset and risk free asset, and a portfolio with two risky assets we can find the optimal risky portfolio.
Finding the Optimal Risky Portfolio/Maximize the slope of the CAL a) Find Weight D: Weight D =
(𝐸
(𝑟𝑑)
(𝐸
(𝑟𝑑)
− 𝑟 𝑓
)𝜎
2
𝐸
−(𝐸
(𝑟𝑒)
−𝑟 𝑓
)∗𝐶𝑂𝑉
(𝑟𝑑,𝑟𝑒)
− 𝑟 𝑓
)𝜎
2
𝐸
+ (𝐸
(𝑟𝑒)
−𝑟 𝑓
)𝜎
2
𝐷
−(𝐸
(𝑟𝑑)
−𝑟 𝑓+
𝐸
(𝑟𝑒)
−𝑟 𝑓
)𝐶𝑂𝑉
(𝑟𝑑,𝑟𝑒) b) Find Weight E: 1 – Weight D c) Plug in weights into the reward – variance slope equation using returns and standard deviation from the portfolio with two risky assets
Arriving at the optimal Complete Portfolio
1) Specify the exact values used for the variables (expected return, standard deviation, covariance)
2) Find the optimal Risky Portfolio a) Use the following Equation to find the weights
Find Weight D: Weight D =
(𝐸
(𝑟𝑑)
(𝐸
− 𝑟 𝑓
)𝜎
2
𝐸
(𝑟𝑑)
− 𝑟
+ (𝐸
(𝑟𝑒) 𝑓
)𝜎
2
𝐸
−𝑟 𝑓
−(𝐸
(𝑟𝑒)
−𝑟
)𝜎
2
𝐷
−(𝐸
(𝑟𝑑) 𝑓
)∗𝐶𝑂𝑉
(𝑟𝑑,𝑟𝑒)
−𝑟 𝑓+
𝐸
(𝑟𝑒)
−𝑟 𝑓
)𝐶𝑂𝑉
(𝑟𝑑,𝑟𝑒)
Find Weight E: 1 – Weight D b) Find the expected return and standard deviation using the formulas from a portfolio with two risky assets 𝜎 2 𝑝
𝐸(𝑟 𝑝
) = 𝑤
𝐷
𝐸(𝑟
𝐷
) + 𝑤
𝐸
𝐸(𝑟
𝐸
)
= 𝑤
2
𝐸 𝜎
2
𝐷
+ 𝑤
2
𝐸 𝜎
2
𝐸
+ 2𝑤
𝐷 𝑤
𝐸
𝐶𝑂𝑉( 𝑟𝑑,𝑟𝑒
) c) Plug in the values into the reward-variance slope formula. THIS YIELDS “Y” which is the percentage that should be invested in the risky portfolio the rest goes into the risk free
asset

𝐸(𝑟 𝑝
) − 𝑅 𝑓 𝜎 𝑝
When two assets are perfectly negatively correlated, you can use the following formula to find the weights of each (set the standard deviation to 0):
Section 6.4 – The Markowitz Portfolio Selection Model
*Go to page 184 for a good illustration of the Markowitz Portfolio Theory
To calculate the optimal portfolio you need the expected return, variance, covariance and the weight of each security.
Portfolio Variance:
1 𝑛
Section 7.1 – The Capital Asset Pricing Model
2 𝑛 − 1 𝑛
̅̅̅̅̅̅
Capital Asset Pricing Model: Is a set of predictions concerning equilibrium expected returns on risky assets 𝛽 𝑖
=
𝐶𝑜𝑣 (𝑟 𝜎 2
𝑀 𝑖
, 𝑟 𝑚
)
CAPM Assumptions:
1) There are many investors, each with an endowment that is small compared to the total endowment of all investors (Participants are price-takers and do not affect the price with their own trades)
2) All investors plan for one identical holding period
3) Investments are limited to a universe of publicly traded financial assets, such as stocks and bonds, and to risk-free borrowing or lending arrangements
4) Investors pay no taxes and not transaction costs
5) All investors are rational mean-variance optimizers, meaning they all use the Markowitz portfolio selection model
6) All investors analyze securities in the same way and share the same economic view of the world
CAPM implies that as individuals attempt to optimize their personal portfolios, they each arrive at the same portfolio, with weights on each asset equal to those of the market portfolio.

The market portfolio includes all stocks in a given set, because we assume that all investors hold the same “optimal portfolio” which means that if a stock is too expensive its price will free fall and will eventually be cheap enough to buy.
Separation Property: A separation property is a crucial element of modern portfolio theory that gives a portfolio manager the ability to separate the process of satisfying investing clients' assets into two separate parts. The first part is the determination of the "optimum risky portfolio". This portfolio is the same for all clients. The second part is tailoring the use of that portfolio to the risk-aversive needs of each individual client.
Mutual Fund Theorem: An investing theory, postulated by Nobel laureate James Tobin, that states that all investors should hold an identically comprised portfolio of "risky assets" combined with some percentage of risk-free assets or cash. A conservative investor would hold a higher percentage of cash, but would have the same basket of risky investments in his or her portfolio as an aggressive investor.
Risk Reward Ratio for a Stock =
𝐸
(𝑟𝑏)
−𝑟
𝐶𝑜𝑣(𝑟 𝑏 𝑓
,𝑟 𝑚
)
Risk Reward Ratio for the Market Portfolio =
𝐸(𝑟 𝑚
)−𝑅 𝑓 𝜎 2 𝑚
*The two should be equal because all stocks in the market portfolio are in equilibrium
Using these assumptions you get the famous CAPM assumptions:
𝐸
(𝑟𝑏)
= 𝑟 𝑓
+ 𝛽 𝑏
[𝐸
(𝑟𝑚)
− 𝑟 𝑓
]
Security Market Line (SML):
1) uses the above risk premium as its slope and is valid for both efficient portfolios and individual assets
2) Same as Capital allocation but uses Beta as the horizontal axis
3) Stocks which are overvalued lie under the SML, those which are undervalued lie above.
4) The difference between a company’s expected return and the SML is the securities’ alpha.
Section 8.1 – A Single-Factor Security Market
Input List for the Markowitz Model:
We need:
 N estimates of expected returns
 N estimates of variances
 (N^2 – N) / 2 estimates of covariance

Input list for the single index model:
Each analyst must provide the expected return, variance and the unique risk of the stock OR its beta and the unique risk of the stock
Each Macro analyst must provide us with an expected return for the market and the variance of the market
Single Index Model
𝑅 𝑖
(𝑡) = 𝑎 𝑖
+ 𝛽 𝑖
𝑅 𝑚
(𝑡) + 𝑒 𝑖
(𝑡)
𝐸𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 𝑉𝑎𝑙𝑢𝑒
T-Value =
𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝐸𝑟𝑟𝑜𝑟 𝑉𝑎𝑙𝑢𝑒
If t > 0 value cannot be 0
If t < 0 value can be 0
Single Factor Model: 𝜎 𝑖
2
= 𝛽 𝑖
2 𝜎 2 𝑚
+ 𝜎 2 (𝑒 𝑖
)
𝐶𝑜𝑣
(𝑟𝑖,𝑟𝑗)
= 𝛽 𝑖 𝛽 𝑗 𝜎 2 𝑚 𝜎 2 𝑝
= 𝛽 2 𝑝 𝜎 2 𝑚
+ ∑ 𝑥 𝑖
2
∗ 𝜎 2 (𝑒 𝑖
)

Morgan Stanley Adjusted Beta:
𝐴𝑑𝑗𝑢𝑠𝑡𝑒𝑑 𝐵𝑒𝑡𝑎 =
2
3
(𝑠𝑎𝑚𝑝𝑙𝑒 𝑏𝑒𝑡𝑎) ∗
1
3
(𝑚𝑎𝑟𝑘𝑒𝑡 𝑏𝑒𝑡𝑎 𝑖𝑠 1)
Expected Return-Beta Relationship
𝐸(𝑅 𝑖
) = 𝑎 𝑖
+ 𝛽 𝑖
𝐸(𝑅 𝑚
)
Estimate of Beta:
𝐸𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 𝑉𝑎𝑙𝑢𝑒 − 𝐻𝑦𝑝𝑜𝑡ℎ𝑒𝑠𝑖𝑧𝑒𝑑 𝑉𝑎𝑙𝑢𝑒
𝑆𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝐸𝑟𝑟𝑜𝑟
R-Squared = 1 − 𝜎
2
(𝑒) 𝜎 2
Securities Market Line:
Y intercept is alpha
Slope equals beta