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From individual assets to financial portfolios

When we invest in a financial asset over a period of time, we receive a return on this asset. This return can be positive, in which case we make a profit, or the return can be negative, in which case we make a loss.

When we hold more than one asset, we have a portfolio. The overall return on the portfolio will depend on the returns on the individual assets. But how can we compute the return on the portfolio on the basis of the returns on the assets?

Let’s consider an example. Suppose that you invest in two assets, let’s say asset and asset . These could be stocks issued by two companies. We can denote the return on asset by and the return on asset by . For instance, if the return on is 10% then = 10% = 0.10. If the return on asset is negative, we would be making a loss on holding that asset: for instance, if = –5% = –0.05 our loss on asset will be 5 per cent of the amount which we have invested in the asset.

So, we are making a profit on asset but a loss on asset . Are we making a profit or a loss on our portfolio which includes both and ?

That depends on the composition of our portfolio, that is, on the relative proportions of and in our portfolio. Intuitively, if our portfolio mostly consists of asset we would be making a profit, but if we are mostly holding asset then we could be making a loss overall. If we hold and in equal proportions, we would be making a profit because 10% is greater than 5%.

Can we be more precise?

Let us denote the return on the portfolio by . If the assets and are held in equal proportions, then half of our investment is in and half in . The proportion of each asset in the portfolio is ½. The return on the portfolio is therefore:

The return on the portfolio is 2.5% and we would be making a profit.

In general, if the proportion of asset is and the proportion of asset is , then the return on the portfolio is given by:

In words, to calculate the return on the portfolio, the return on each asset is multiplied by the proportion of the asset in the portfolio. We also call and the weights on each asset in the portfolio.

For instance, if = 0.75 and = 0.25, then

and we would still be making a profit. If instead = 0.20 and = 0.80, then

and we would be making a loss.

Finally, what do you notice about the proportions or weights of the assets in the portfolio? In each of our examples they always add up to one

Can you see why this is so? Use the comments section to share your thoughts with your fellow learners.

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This article is from the free online course:

Risk Management in the Global Economy

SOAS University of London