Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Portfolio Optimization: Models and Strategies

In course

MGT-418: Convex optimization

This course introduces the theory and application of modern convex optimization from an engineering perspective. ...

Description

This lecture by the instructor covers portfolio optimization under uncertainty, focusing on various decision criteria such as expected value, variance, value-at-risk, and conditional value-at-risk. Different models are presented, including mean-variance functional and value-at-risk minimization, highlighting their implications and practical performance.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Instructor

Daniel Kuhn

Official source

Ontological neighbourhood

Statistics

Statistical inference: Mathematical statistics

Business

Business administration: Risk management

Related concepts (32)

Expected shortfall

Expected shortfall (ES) is a risk measure—a concept used in the field of financial risk measurement to evaluate the market risk or credit risk of a portfolio. The "expected shortfall at q% level" is the expected return on the portfolio in the worst of cases. ES is an alternative to value at risk that is more sensitive to the shape of the tail of the loss distribution. Expected shortfall is also called conditional value at risk (CVaR), average value at risk (AVaR), expected tail loss (ETL), and superquantile.

Modern portfolio theory

Modern portfolio theory (MPT), or mean-variance analysis, is a mathematical framework for assembling a portfolio of assets such that the expected return is maximized for a given level of risk. It is a formalization and extension of diversification in investing, the idea that owning different kinds of financial assets is less risky than owning only one type. Its key insight is that an asset's risk and return should not be assessed by itself, but by how it contributes to a portfolio's overall risk and return.

Value at risk

Value at risk (VaR) is a measure of the risk of loss of investment/Capital. It estimates how much a set of investments might lose (with a given probability), given normal market conditions, in a set time period such as a day. VaR is typically used by firms and regulators in the financial industry to gauge the amount of assets needed to cover possible losses. For a given portfolio, time horizon, and probability p, the p VaR can be defined informally as the maximum possible loss during that time after excluding all worse outcomes whose combined probability is at most p.

Entropic value at risk

In financial mathematics and stochastic optimization, the concept of risk measure is used to quantify the risk involved in a random outcome or risk position. Many risk measures have hitherto been proposed, each having certain characteristics. The entropic value at risk (EVaR) is a coherent risk measure introduced by Ahmadi-Javid, which is an upper bound for the value at risk (VaR) and the conditional value at risk (CVaR), obtained from the Chernoff inequality. The EVaR can also be represented by using the concept of relative entropy.

Tail value at risk

Tail value at risk (TVaR), also known as tail conditional expectation (TCE) or conditional tail expectation (CTE), is a risk measure associated with the more general value at risk. It quantifies the expected value of the loss given that an event outside a given probability level has occurred. There are a number of related, but subtly different, formulations for TVaR in the literature. A common case in literature is to define TVaR and average value at risk as the same measure.

Related lectures (55)

Quantitative Risk Management: Risk Measures

Covers risk measures used for determining risk capital and capital adequacy.

Risk Measures: VaR and ES

Explores Value-at-Risk and Expected Shortfall as key risk measures in financial risk management.

Risk Measures: Accuracy and Multivariate Distributions

Discusses risk measure evaluation, confidence intervals, and multivariate distributions for portfolio risk assessment.

Quantitative Risk Management: VaR and ES

Covers Value at Risk (VaR) and Expected Shortfall (ES) in risk management, including backtesting and multivariate distributions.

Aggregate Risk: Coherent Risk Measures