Yesterday, I covered return calculation for a portfolio with leverage. To review, the background information is:

- The investor wants to acquire a 500 million euro property but only has 400 million in cash
- The investor borrows 100 million euro in order to acquire the property; cost of borrowing is 5% per year.
- Over a one year period, the property appreciates in value by 40 million.

In this example, the cash basis return is 8%, and the leveraged return is 8.75%. If you would like to review how these returns are determined, please see the previous post here.

So to summarize, by using leverage, the investor has amplified the return of 8% (the cash basis return the investor would realize if they acquired a 400 million euro investment in the 500 million euro property) to realize a levered return of 8.75%.

In this post, I look at contribution to see the relationship between the investment and the leverage, with respect to return impact.

Recall that the return of a portfolio is the sum of the contribution from all of the positions in the portfolio:

In this portfolio, there are two positions:

- The real estate investment, which earns a return of 8%
- The cash borrowed, which has a cost of 5%

The 500 million euro real estate investment constitutes a weight of 125% of the total portfolio value of 400 million euro at the start of the period, Thus, the return contribution of this position is 10%, which is the weight of 125% multiplied by the return of 8%.

The cash obligation (the borrowed cash of 100 million euro) has a weight of -25% of the total portfolio. The return on this position is the interest cost of 5%. Thus, the contribution of the leverage is -25% multiplied by 5% which equals -1.25%.

The portfolio return is, therefore, the sum of the contribution from the positions: 10% plus -1.25% is the same 8.75% that we calculated using portfolio values in the previous blog post.

The data for the return contributions are shown here, to summarize:

Hopefully this second view into the calculation of portfolio return helps you to understand how leverage can amplify returns. From a contribution standpoint, the use of leverage has been effective because:

- the underlying assets constitute more than 100% of the portfolio value, which increases the contribution from 8% to 10%
- the cash borrowed is a short position, so the interest cost will erode the contribution amplification from the underlying assets. But, because the interest cost of 5% is less than the 8% return of the underlying assets, there is still a benefit to the use of leverage. The contribution of the leverage is -1.25%, eroding the 10% contribution from the underlying assets, resulting in an overall contribution of 8.75%. Thus, there was a 75 basis points benefit in this example due to the use of leverage.

Happy studying!