Mean-Variance Framework Risk & Return Models

From the Vaults – Aswath Damodaran: Risk & Return Models

From the Vaults – Aswath Damodaran: Risk & Return Models

Risk & Return Models: First Principles

Invest in projects that yield a return greater than the minimum acceptable hurdle rate.

  • The hurdle rate should be higher for riskier projects and reflect the financing mix used – owners’ funds (equity) or borrowed money (debt)
  • Returns on projects should be measured based on cash flows generated and the timing of these cash flows; they should also consider both positive and negative side effects of these projects.

Choose a financing mix that minimizes the hurdle rate and matches the assets being financed.

If there are not enough investments that earn the hurdle rate, return the cash to stockholders.

  • The form of returns – dividends and stock buybacks – will depend upon the stockholders’ characteristics.

Objective: Maximize the Value of the Firm

Basic Questions of Risk & Return Model

  • How do you measure risk?
  • How do you translate this risk measure into a risk premium?

What is Risk?

Risk, in traditional terms, is viewed as a ‘negative’. Webster’s dictionary, for instance, defines risk as “exposing to danger or hazard”. The Chinese symbols for risk, reproduced below, give a much better description of risk

The first symbol is the symbol for “danger”, while the second is the symbol for “opportunity”, making risk a mix of danger and opportunity.

The Capital Asset Pricing Model

  • Uses variance as a measure of risk
  • Specifies that only that portion of variance that is not diversifiable is rewarded.
  • Measures the non-diversifiable risk with beta, which is standardized around one.
  • Translates beta into expected return – Expected Return = Riskfree rate + Beta * Risk Premium
  • Works as well as the next best alternative in most cases.

The Mean-Variance Framework

The variance on any investment measures the disparity between actual and expected returns.

Mean-Variance Framework Risk and Return Models

The Importance of Diversification: Risk Types

The risk (variance) on any individual investment can be broken down into two sources. Some of the risk is specific to the firm, and is called firm-specific, whereas the rest of the risk is market wide and affects all investments.

The risk faced by a firm can be fall into the following categories –

  • (1) Project-specific; an individual project may have higher or lower cash flows than expected.
  • (2) Competitive Risk, which is that the earnings and cash flows on a project can be affected by the actions of competitors.
  • (3) Industry-specific Risk, which covers factors that primarily impact the earnings and cash flows of a specific industry.
  • (4) International Risk, arising from having some cash flows in currencies other than the one in which the earnings are measured and stock is priced
  • (5) Market risk, which reflects the effect on earnings and cash flows of macro economic factors that essentially affect all companies

Risk & Return Models: The Market Portfolio

Assuming diversification costs nothing (in terms of transactions costs), and that all assets can be traded, the limit of diversification is to hold a portfolio of every single asset in the economy (in proportion to market value). This portfolio is called the market portfolio.

Individual investors will adjust for risk, by adjusting their allocations to this market portfolio and a riskless asset (such as a T-Bill) Preferred risk level Allocation decision

  • No risk 100% in T-Bills
  • Some risk 50% in T-Bills; 50% in Market Portfolio;
  • A little more risk 25% in T-Bills; 75% in Market Portfolio
  • Even more risk 100% in Market Portfolio
  • A risk hog.. Borrow money; Invest in market portfolio;

Every investor holds some combination of the risk free asset and the market portfolio.

Risk & Return Models: The Risk of an Individual Asset

The risk of any asset is the risk that it adds to the market portfolio

Statistically, this risk can be measured by how much an asset moves with the market (called the covariance)

Beta is a standardized measure of this covariance

Beta is a measure of the non-diversifiable risk for any asset can be measured by the covariance of its returns with returns on a market index, which is defined to be the asset’s beta.

See full Aswath Damodaran: Risk & Return Models in PDF format here via CSInvesting


Saved Articles

The Life and Career of Charlie Munger

Charlie is more than just Warren Buffett’s friend and Berkshire Hathaway’s Vice Chairman – Buffett has actually credited him with redefining how he looks at investing. Now you can learn from Charlie firsthand via this incredible ebook and over a dozen other famous investor studies by signing up below:

  • Learn from the best and forever change your investing perspective
  • One incredible tidbit of knowledge after another in the page-turning masterpiece of a book
  • Discover the secrets to Charlie’s success and how to apply it to your investing
Never Miss A Story!
Subscribe to ValueWalk Newsletter. We respect your privacy.

Are you an intelligent investor?

ValueWalkPremium is a website and newsletter for smart investors like yourself. We focus on the latest hedge fund industry news much of which is not in the public domain and obtained via our sources.

We also have 10 years of resources on how to use this information to better your investment process.

Sign up for  today for only a few dollars a day and get a 3 day no obligation trial with a targeted 20% discount coupon code.

Cancel anytime during trial and you are never charged.

Limited time offer: For first 50 subscribers