Friday, December 27, 2013

Understanding Financial Leverage

Recently, friends mentioned that their periodic meeting with their investment advisor happened to coincide with their decision to purchase a new car. The investment advisor recommended that they take the dealer’s 0.9% financing because “our portfolio is doing a lot better than that.”

Which ignores the point that taking out the loan will leverage their portfolio. If levering up portfolio returns was such a good thing, why had they not discussed that as a strategy before? Investments exist that can provide leverage without the portfolio itself borrowing money.

So, back to my friends’ situation.

Looking only at long-term averages, borrowing at 0.9% to invest in the markets is a winner. After all, any reasonable mix of stocks and bonds has done much better than that over the last few years, and is expected to earn more than 0.9% for any given future year. Unfortunately every year is unique; averages are only the place from which standard deviations start, not the actual results.

For discussion purposes only, and not to reflect my friends’ actual finances (of which I have no knowledge), let’s assume a balanced portfolio of 60% stocks and 40% bonds, and that the price of the car is equal to 5% of the portfolio value. Here are two alternatives:
  1. Sell off 5% of the portfolio and buy the car in cash.
  2. Borrow 5% of the portfolio from the dealer at 0.9% and each month sell enough of the portfolio to make the car payment.
The actual car loan in this case was for three years. For simplicity, let’s look instead at a 1-year loan with a lump sum payment due at the end of 2014. This changes the actual facts, but does not affect an understanding of how this leveraging will work. The actual return of the portfolio in 2014 as a percentage of assets can be designated as R.

The value of the portfolio at the end of 2014 using the pay-in cash-approach will be  P1 = [.95 *P0 * (1+R)]

And taking the 0.9% car loan the value of the portfolio at the end of 2014 will be:    P1 = P0 * (1+R) - .05 * P0 * (1.009) = .95 * P0 * (1+R) + .05 * P0 * (1+R - 1.009)  = [.95 * P0 * (1+R)] + .05 * P0 * (R - .009)

Comparing these two scenarios, we see mathematically what we logically knew all along: as long as the actual return (R) beats the 0.9% financing cost of the loan, we’re ahead. Mathematically, this shows as difference between the two formulae: .05 * P0 * (R - .009)

Paying cash and eschewing the car loan, my friends were going to have a portfolio that went up or down solely based on their asset mix. By taking the loan, my friends now changed their results. If the portfolio earned more than 0.9% for the year, they would end up with more money at the end of the year. Conversely, if the portfolio did not earn the 0.9% threshold, they would have a lower portfolio value than would have been the case without the loan.

This is what leveraging does. Given the loan is equal to 5% of the portfolio, by taking the loan rather than paying in cash, we have (1.00/.95) = 1.0526 times the earning power before we have to pay off the loan.

What are the chances that 2014 won’t provide an investment return of at least 0.9%? I’ll tell you for sure on December 31, 2014. In the meantime we can look at past results as an indication of what 2014 may bring. According to [] there is a 35% chance of a balanced portfolio losing value in any given year. The maximum one-year loss on a balanced portfolio (so far) has been 35%. That would feel terrible, but after taking the loan we’ll actually lose closer to 37%.

Of course the best year in the past produced a gain of 89%, which with the leverage would increase to almost 93.6%.

In most years, the investment return will range between plus or minus 10%, which with leverage translate to a range of -10.6% to +10.5%. The loan/no loan difference is hardly earth shattering. Due to the law of diminishing returns, the extra gain caused by increased leverage won’t make us feel much better. If the markets went up 89%, we would only feel marginally better earning 94%. However, if we lose more money than we otherwise would have—especially those of us who are retired and don’t have the ability to replace lost investments through earnings, that can hurt. It hurts a bit monetarily, but even more psychologically. We tend to beat ourselves up about bad decisions much more than we give ourselves credit for good decisions.

Everyone can make their own choice about leverage. As a retiree with a sufficient portfolio to live in a manner that is acceptable to me, my risk concerns revolve around bad things happening to my portfolio, not whether someone else made more money than I did in the market.

It won’t surprise you that I paid cash for my car.

~ Jim

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