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!