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Panos Parpas Single Period Markowitz Model 381 Computational Finance Imperial College London

Topics Covered ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Terminology ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],relative frequency finite number of possibilities Expected value of squared variable how much y tends to vary from its mean

Terminology ,[object Object],[object Object],sign defines direction of the relationship

Asset Returns ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Portfolio Return ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Portfolio Return ,[object Object],[object Object]

Example ,[object Object],[object Object],[object Object],root represents today future uncertainty is discretised by 3 events (states)

Example: Expected Returns ,[object Object],[object Object],[object Object],[object Object]

Risk ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Diversification ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Portfolio Risk For n securities, portfolio risk – variance of the portfolio return Expected value of squared variable- how much rate of return of portfolio tends to vary from its mean

Example: Variance of Portfolio ,[object Object]

Example: Variance of Portfolio ,[object Object],For equally weighted portfolio

Short Sale ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example:Short-sale ,[object Object],[object Object],[object Object],Make Money Lose Money RISKY: no guarantee that the price of a short stock will drop

Optimal Portfolio ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Maximize (expected return of portfolio) (weighted sum of individual expected rates of return) Minimize (portfolio risk) (expected value of squared variable- how much rate of return of portfolio tends to vary from its mean)

The Markowitz Model ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Maximum Expected Wealth Problem ,[object Object]

Minimum Variance Portfolio ,[object Object]

Mean-Variance Optimisation Problem ,[object Object],[object Object]

Efficient Frontier ,[object Object],[object Object]

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