# Tag Archives: Open Yale Courses

## Portfolio Diversification and Supporting Financial Institutions (CAPM Model)

2013.05.10 , , Portfolio Diversification and Supporting Financial Institutions (CAPM Model)已关闭评论 , 4,501 views
##### Overview:

Portfolio diversification is the most fundamental concept of risk management. The allocation of financial resources in stocks, bonds, riskless, assets, oil and other assets determine the expected return and risk of a portfolio. Taking account of covariances and expected returns, investors can create a diversified portfolio that maximizes expected return for a given level of risk. An important mission of financial institutions is to provide portfolio-diversification services.

Fabozzi et al. Foundations of Financial Markets and Institutions, chapters 8 and 13

Jeremy Siegel, Stocks for the Long Run, chapters 1 and 2

Optimal Portfolio Diversification

in General Case

Drop assumption of equal weighting, independence and equal variance

Put xi dollars in i th asset, I=1,..,n, where the xi sum to \$1.

Portfolio expected value

Portfolio variance (two assets) =

Beta

The CAPM implies that the expected return on the ith asset is determined from its beta.

Beta (i) is the regression slope coefficient when the return on the ith asset is regressed on the return on the market.

Fundamental equation of the CAPM:

## Technology and Invention in Finance

2013.04.21 , , Technology and Invention in Finance已关闭评论 , 1,835 views
##### Overview:

Technology and innovation underlie finance. In order to manage risks successfully, particularly long-term, we must pool large amounts of risk among many, diverse people and overcome barriers such as moral hazard and erroneous framing. Inventions such as insurance contracts and social security, and information technology all the way from such simple things as paper, and the postal service to modern computers have helped to manage risks and to encourage financial systems to address issues pertaining to risk. The tax and welfare system is one of the most important risk management systems.

## The Universal Principle of Risk Management: Pooling and the Hedging of Risks

2013.04.21 , , The Universal Principle of Risk Management: Pooling and the Hedging of Risks已关闭评论 , 1,906 views
##### Overview:

Statistics and mathematics underlie the theories of finance. Probability Theory and various distribution types are important to understanding finance. Risk management, for instance, depends on tools such as variance, standard deviation, correlation, and regression analysis. Financial analysis methods such as present values and valuing streams of payments are fundamental to understanding the time value of money and have been in practice for centuries.

Probability P, 0<P<1
• Multiplication rule for independent events: Prob(A and B) = Prob(A)*Prob(B)
• Probability of n independent accidents = P^n
• Probability of x accidents in n policies (Binomial Distributon):

Expected Value, Mean, Average

Variance and Standard Deviation

• Variance (^2)is a measure of dispersion
• Standard deviation is square root of variance

Covariance
• A Measure of how much two variables move together

Correlation
• A scaled measure of how much two variables move together

Present Discounted Value (PDV)
• PDV of a dollar in one year = 1/(1+r)
• PDV of a dollar in n years = 1/(1+r)^n
• PDV of a stream of payments x1,..,xn

Consol and Annuity Formulas
• Consol pays constant quantity x forever
• Growing consol pays x(1+g)^(t-1) in t
• Annuity pays x from time 1 to T