The provided articles offer insights into constructing an optimal investment portfolio, including mathematical and programming techniques like mean-variance optimization, efficient frontier, lagrangian multipliers, etc. Proper risk management through diversification, asset allocation, immunization strategies are also discussed. Practical examples using stocks, bonds and other securities demonstrate portfolio optimization approaches in depth. The key focus is on minimizing risk while maximizing returns.
Mean-variance framework minimizes volatility while improving reward-to-risk ratio
The articles explain how to minimize portfolio variance and find efficient frontier using statistical properties like expected returns, volatility, correlations and covariance matrix. Techniques like lagrangian optimization, taking derivatives to find minimum points are covered. The goal is to maximize reward per unit of risk taken.
Liability driven strategies ensure portfolios satisfy future obligations
Immunization strategies are liability driven techniques that structure bond portfolios to satisfy future liabilities. Different constructions using variable coupon rates, maturities and market assumptions are analyzed to make portfolios immune to interest rate changes. Rebalancing also ensures meeting multiple liability payment obligations.
Tangent portfolios optimize risk-adjusted returns for a given risk level
The capital allocation line plots optimal portfolio combinations for a given risk-free rate. The point where this line is tangent to the efficient frontier offers highest returns per unit of risk. Margin trading and short selling pushes the efficient frontier upwards to improve returns at any desired risk tolerance.
In summary, the articles provide various quantitative techniques to optimize investment portfolios by balancing risk and returns. Mathematical and programming tools combined with market data on asset classes lead to improved portfolio construction.