Investments

An index and a few stocks, what is the best mix?

Name: Business Tutor
Address: Burnaby, BC, CA
Telephone: +1-604-916-5838
Price range: C$30–C$129

Separate market risk from firm-specific surprises, then build the optimal risky portfolio using an index and analysed stocks. Solve has 10 questions with editable givens and worked answers.

A simpler model · Step 1 of 12

One index can replace a web of covariances

Full modelIndex model

A simpler model · Step 1 of 12

One index can replace a web of covariances

A portfolio forecast needs expected returns and an account of how securities move together. The full covariance approach forecasts every pair; the single-index model links each stock to the same market index. Start by comparing their input counts. The index model needs fewer estimates with at least five securities; with four the counts match, and with fewer the full approach needs fewer.

Try it: Change the number of stocks, including small portfolios.

Number of securities20

Full model

230

Index model

Full minus index

168

Full model = n returns + n variances + n(n − 1) ÷ 2 covariances.

(20 + 20 + (20 × (20 − 1) ÷ 2)) = 230 estimates.

Index model = n alphas + n betas + n residual variances + market premium + market variance.

((3 × 20) + 2) = 62 estimates.

Full minus index = (230 − 62) = 168. The index model needs fewer estimates.

Check yourself

Which forecasts grow with the number of distinct stock pairs in the full approach?

Exam coming up and alpha, beta and residual risk still blur together?

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An index and a few stocks, what is the best mix?

One index can replace a web of covariances

One index can replace a web of covariances

Count the forecasts needed

Exam coming up and alpha, beta and residual risk still blur together?

Questions, answered.

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