BUS 315

Two funds, one best mix

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

Combine a bond fund and a stock fund, see how much risk cancels out, find the efficient frontier, then let T-bills pick the one risky portfolio every investor should hold.

Part 1 · Why combine assets · Step 1 of 12

Spread money over more stocks: some risk goes, some stays

portfolio SDmarket-risk floor, 15.65%if the stocks were unrelated (correlation 0)

Some risk belongs to one company: a product recall, a lost customer, a lucky discovery. This firm-specific risk (also called diversifiable risk) gets spread thin when you own many stocks. Other risk hits most companies at once: a recession or a jump in interest rates. That market risk (systematic risk) stays however many stocks you own. Here every stock has an SD of 35% and your money is split equally across n of them.

Try it: Set the correlation to 0, then push n to 100: risk heads toward zero. Now raise the correlation: the curve flattens out on a floor.

Number of stocks, n10

Correlation between any two stocks0.2

unrelatedmove together a lot

Portfolio SD

18.52%

Floor with many stocks

15.65%

Firm-specific share of variance

28.6%

With 10 stocks, 71.4% of the variance is market risk that no amount of diversifying removes. Past about 30 stocks the curve is almost flat.

Average covariance = 0.2 × 0.35² = 0.0245

How much any two stocks move together: correlation × variance.

σ_P² = 0.35² ÷ 10 + (10 − 1) ÷ 10 × 0.0245 = 0.0343, so σ_P = 18.52%

The first part shrinks as n grows; the weight on the covariance heads to 1.

Floor = √0.0245 = 15.65%

With a huge number of stocks only the covariance is left.

Check yourself

Every stock has an SD of 40% and every pair has a correlation of 0.36. With a very large number of equally weighted stocks, the portfolio SD gets close to…

Question 1 of 5CoreTutorial question from the slides

Two new funds: a 50/50 mix, the minimum-variance mix and a target return

Two funds are on offer for the coming year: a bond fund D with expected return 6% and SD 10%, and a stock fund E with expected return 12% and SD 20%. The correlation between them is 0. Short sales are not allowed.

Find the expected return and SD of a portfolio split 50/50 between the two funds.
Find the minimum-variance portfolio G: its weights, expected return and SD.
What weight in E gives an expected return of 9%?
Does G dominate the 50/50 portfolio?
What extra information would help choose between efficient portfolios?

Given

The two funds

	Expected return	SD
Bond fund D	6%	10%
Stock fund E	12%	20%

Between the funds

Correlation of D and E0

Target expected return9%

Solution

Every long-only mix of D and E

Read the question and the givens first. Try the first part yourself, then press Start solving and open the working to check.

a. 50/50 expected return

a. 50/50 SD

b. Weight in E at G

b. G: return / SD

c. Weight in E for the target

d. G dominates 50/50?

Exam coming up and the efficient frontier still feels slippery?

Bring your problem sets. We work through them together until every type feels routine.

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Two funds, one best mix

Spread money over more stocks: some risk goes, some stays

Two new funds: a 50/50 mix, the minimum-variance mix and a target return

Exam coming up and the efficient frontier still feels slippery?

Questions, answered.

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How do I book, and how do I know it is confirmed?

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