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11.2 Portfolios

PLEASE NOTE: This book is currently in draft form; material is not final.

Learning Objectives

1. Calculate the returns for a portfolio of securities.
2. Explain the benefits of diversification.

Determining the risk of holding a single asset is a difficult task in itself. In reality, investors will typically hold many different assets of potentially different types. Another common alternative is that investors hand their money over to a manager that pools all the investors’ contributions to purchase such, which we call a portfolioA collection of financial assets. (a collection of financial assets).

While individual stocks or bonds might rise or fall in value, ultimately an investor cares about the performance of the whole portfolio. If we make one bad investment but five good ones, we might come out ahead and be satisfied. Since investors tend to hold stocks as parts of their portfolios, managers need to understand how their company’s performance will affect the risk and return of the portfolio.

Determining the return of the portfolio is a simple matter of taking the average of the returns of the components, weighted by the portion of the portfolio initially invested in each. Thus, if we invest \$20 thousand in ABC stock and \$80 thousand in FEG stock, our weights would be 20/(20+80) = 20/100 = .2 and 80/(20+80) = 80/100 = .8, respectively.

Equation 11.3 Portfolio Return (weighted mean)

Portfolio Return = (weight of security 1 × rate of return of security 1) + (weight of security 2 × rate of return of security 2) + … + (weight of security n × rate of return of security n) = w1r1 + w2r2 + … + wnrn

If the return on ABC was 10% and the return on FEG was −2%, the return of our portfolio would be (.2 × .10) + (.8 × −.02) = .004 or 0.4%. We can confirm that this is correct: we earn 10% on our \$20 thousand investment for a return of \$2 thousand, and we lose 2% on our \$80 thousand investment for a return of −\$1,600. Adding the returns together gives a positive \$400, which is precisely 0.4% of our original \$100 thousand investment.

Notice that our portfolio return lies somewhere between the two extremes. Almost always, some investments will do better than others, so that our portfolio’s returns won’t be as good as our best investments. But the benefit is that our portfolio’s returns won’t be as bad as our worst investments. This is the key to diversificationHolding a portfolio of different assets so as not to concentrate exposure on one particular asset. (holding a portfolio of different assets so as not to concentrate exposure on one particular asset). This is embodied by the old saying, “Don’t put all your eggs in one basket.” Diversification can lower risk to a point, and is the closest thing to a “free lunch” in finance! To see this more concretely, we need to have a specific measure for our risk, which we will introduce later in this chapter.

Key Takeaways

• Portfolio returns are a weighted (by % of investment) average of the components.
• Diversification causes the portfolio’s returns to be less extreme than our best or worst investments.

Exercises

1. We have 30% invested in JKL stock, 40% in MNO stock, and 30% in PQR stock. Returns are 2%, 5%, and −1% respectively. What was our portfolio’s return?
2. We have \$25 thousand invested in ABC stock, \$50 thousand in DEF stock, and \$15 thousand in GHI stock. What are the portfolio weights?
3. ABC returned 10%, DEF returned 5%, and GHI returned 7%. Given the weights in #2, what is our portfolio’s return?