What you will learn
- Define a portfolio and the weight of an asset
- Calculate a portfolio's return as a weighted average
- Understand why investors hold portfolios instead of single assets
- See how the weights shape a portfolio's character
Unit 5 gave you the statistical tools: return, risk, correlation. This unit puts them to work building real portfolios and managing risk. Some of it gets involved, so we start at the very beginning and build up carefully. And the beginning is a simple question that everything else rests on: what exactly is a portfolio, and how do you describe one with numbers?
A portfolio is just your whole collection of investments
A portfolio is the entire set of investments you hold, considered together as one thing. Instead of owning a single stock, you own a mix: perhaps several stocks, some bonds, a fund, and a bit of cash. That whole bundle is your portfolio. This unit is really one long answer to a single question: given all the assets in the world, how should you choose the mix, and how do you manage its risk over time? Before we can optimize a portfolio, we need a way to measure one.
Weights: the fraction in each asset
The main number describing a portfolio is not the dollar amount in each asset but the weight of each asset, meaning the fraction of your total money invested in it. Suppose you have 10,000 dollars and put 4,000 into Stock A. The weight of Stock A is 4,000 divided by 10,000, which is 0.4, or 40 percent. If the other 6,000 goes into Stock B, its weight is 0.6, or 60 percent. Notice the weights add up to 1, or 100 percent, because they account for all of your money. Weights, not dollar amounts, are what determine how the portfolio behaves, which is why we describe portfolios in weights.
Calculating expected portfolio returns and variances (FinanceKid)
Walks through computing a portfolio's return from its weights. Focus on the weighted-average return here. The variance part previews the next lesson.
Key terms
- Portfolio
- The entire collection of investments held together and analyzed as one.
- Weight
- The fraction of the portfolio's total value invested in a given asset. All weights sum to 1.
- Holding
- A single investment inside the portfolio, such as one stock or bond.
- Portfolio return
- The overall return of the whole portfolio, a weighted average of its holdings' returns.
The formula in symbols
- w = each asset's weight
- r = that asset's return
A portfolio's return is the weighted average of the returns of its holdings: multiply each asset's return by how much of it you hold, then add those up. This is the same probability-weighted average idea from Unit 5, except now the weights are the fractions of your money rather than probabilities.
The return of a two-asset portfolio
You put 60 percent of your money in stocks that returned 10 percent this year, and 40 percent in bonds that returned 4 percent. What was your portfolio's return?
- Weight each asset's return. Stocks: 0.6 times 10 percent is 6 percent. Bonds: 0.4 times 4 percent is 1.6 percent.
- Add the weighted returns. 6 percent plus 1.6 percent.
- Read the result. The portfolio returned 7.6 percent.
Why it matters: The portfolio return sits between the stock return (10 percent) and the bond return (4 percent), pulled toward whichever asset carries more weight. A weighted average always lands between its parts.
Calculate a portfolio return
You hold 70 percent in Fund A, which returned 12 percent, and 30 percent in Fund B, which returned 2 percent. What is your portfolio's return, in percent?
Portfolio expected return, standard deviation, covariance (Financial Analyst Network)
A step-by-step calculation of a portfolio's expected return and risk. Good extra practice with the weighted-average idea before we tackle risk next lesson.
Why hold a portfolio at all?
Why not just find the single best stock and put everything there? Two reasons, and they define this entire unit. First, you cannot know in advance which single asset will do best, and concentrating everything in one is a bet that can wipe you out if you are wrong. Second, and more subtly, combining assets that do not move in perfect lockstep can lower your overall risk without lowering your expected return, the free lunch you glimpsed in Unit 5. A portfolio lets you tune your risk and spread your bets, which a single holding never can. The rest of this unit is about doing that well.
| Asset | Amount | Weight |
|---|---|---|
| US stock fund | 5,000 | 0.50 |
| International stock fund | 2,000 | 0.20 |
| Bond fund | 2,000 | 0.20 |
| Cash | 1,000 | 0.10 |
| Total | 10,000 | 1.00 |
Check the weights
An investor holds 3,000 dollars in Stock X and 1,000 dollars in Stock Y, with nothing else. What is the weight of Stock X?
The total is 3,000 plus 1,000, which is 4,000. Stock X's weight is 3,000 divided by 4,000, which is 0.75, or 75 percent.Why weights, not dollars?
In your own words, explain why we describe a portfolio using weights (fractions) rather than dollar amounts.
Write an answer before comparing it with the model response.
Model answer
Weights describe how the portfolio behaves, while dollar amounts just describe its size. Two investors, one with 10,000 dollars and one with 10 million, who both put 60 percent in stocks and 40 percent in bonds have portfolios that rise and fall by the same percentages, even though the dollar values are wildly different. The weights, not the dollars, determine the portfolio's return and risk, so weights are the natural language for comparing and designing portfolios. Weights also always add up to 1, which makes the math of combining assets clean.
You can now describe any portfolio with weights and compute its return. But return is only half the story. The next lesson tackles the harder and more surprising half: a portfolio's risk, which, unlike its return, is not a simple weighted average of the parts.