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LEVERAGE: What, Where and How to Measure



#1 Leverage Basics

#2 Leverage in Company's Capital Structure

#3 Leverage with Split-Share Corps

#4 Leverage with Options

#5 Leverage with Futures Contracts

#6 Leverage with Shorted Stocks

#7 Leverage Within Operations

#8 Academic Paper




#1 LEVERAGE BASICS Top
WHAT
With leverage you magnify the gains and losses of an investment (usually) by borrowing money to increase the amount of assets purchased.
  • The objective is to borrow at interest rates lower than the asset's return, to profit from the differential.
  • Never forget a risky asset's %return may turn out to be lower than the debt's %cost, lowering your returns.
  • The disclosure will say "leveraged X times". This can mean two different things. Usually it equals "Total Investment / Equity". It can also mean "Debt / Equity".

WHERE
  • Individuals can create their own leverage by borrowing money personally. Most people use leverage to buy Real Estate. They hope the mortgage interest rate is lower than the total return on the property. Individuals use leverage to increase the amount of car they drive. They borrow the purchase price even while knowing that the loan's interest rate will be higher than the return from car ownership, because there rarely IS a return from ownership, for a loss they ignore.
  • Investors own the common shares of companies who leverage themselves. Evaluating the risks of that leverage is part of security analysis. The leverage is created two ways.
    (a) The financing of the business can be split between debt and equity at different percentages. The larger the debt percentage the greater the leverage.
    (b) A company's costs of production are fixed and variable. Variable costs create no leverage, but fixed costs allow small changes in Revenues to produce huge changes in Net Income. The larger the fixed costs (as a percent of revenue) the greater the leverage.
  • Structured Products exist as either closed-ended funds, or limited companies, or Income Trusts. Many are responding to the public's demand for yield by leveraging 8-10 times. This is frequently not disclosed ANYWHERE other than on page (eg) 20 of the Prospectus.
  • Stock options and Futures contracts also use leverage to magnify your possible returns (losses). They allow you to take positions with $0 money 'down'.

EXAMPLE
5% Asset's Projected Rate of Return
4% Debt's Interest Rate
8:1 Debt to Equity ratio

                  LONG-FORM MATH
Investment in Assets8+1* 5%=45
less Interest (8)* 4%=(32)
equals Equity1 *13%=13

                  SHORT-FORM GENERIC CALCULATION
Interest Rate Differential5 less 41%
Debt to Equity Multiple8/18
Multiply Line1 * Line2
= 8%
Add Asset's Return
+ 5%
Equals Equity's Return
= 13%

LOSS EXAMPLE
Never, ever forget the possibility of lower than expected asset returns. Leverage is just as punishing on the downside as it is helpful on the upside.

3% Actual Realized Return on Asset
4% Debt's Interest Rate
8:1 Debt to Equity ratio

Interest Rate Differential3 less 4=(1)%
Debt to Equity Multiple8/18
Multiply Line1 * Line2
=(8)%
Add Asset's Return
3%
Equals Equity's Loss
= (5)%

CONCEPTUAL UNDERSTANDING

Knowing the facts does not ensure you 'think about' leverage correctly. A common mistake is to think a) I believe the markets go up in the long term, and b) leverage increases your gains, therefore c) I should borrow for leverage ... WRONG.

Think of the debt interest as a 'HURDLE RATE'. You reap the rewards of leverage only if your asset beats that rate, NOT if it simply goes up in value. You lose when the asset's returns are lower, even though positive. When returns are lower, the normal investor just pockets the returns and bides his time for better days. The leveraged investor is feeling pain each and every day.

The 'better days' may be a long time coming. E.g. the Vancouver real estate market through the 1990's was essentially flat. Owners saw only about 4% returns from rent saved (ignoring rain damage assessments). Through that decade most mortgages were likely above 6% ... ten years of 2% losses.

A PICTURE IS WORTH A THOUSAND WORDS
This chart shows your possible equity returns on the vertical scale. The underlying asset's returns form the horizontal scale. For all three lines, the interest rate on the debt = 5%. See how all the lines rotate around this hurdle rate. The three lines represent different amounts of leverage. The greater the leverage, the greater the slope of the line.
Chart of different returns for different levels of leverage
WHEN LEVERAGE FACTOR QUOTED = "TOTAL INVESTED / EQUITY"

Example: $8 total invested = $4 equity PLUS $4 borrowed = Leveraged Factor 2
It is most common to hear this definition of leverage. It is interpreted to mean "For every dollar increase in the price of the underlying stock, your leveraged play will increase by the leverage multiple." or "For every % increase in the stock, your leveraged play will increase by the % times the leverage multiple."

Begin$GainEndIncrease
Investment in Assets$8$2$1025%
less Interest ($4)ignored($4)
equals Equity$4$2$650%
Leverage Factor2

2

Approaching an understanding from this perspective misses all the implications of the 'HURDLE INTEREST RATE'. As you can see, the interest rate on the debt does not factor into the understanding anywhere. It assumes the debt has 0% interest. Sure it is a simple explanation, but it misses the main points. 'Simple' is rarely 'correct' in any financial understanding.


#2 LEVERAGE IN COMPANY'S CAPITAL STRUCTURE Top

When comparing two possible stocks from the same industry, it is helpful to isolate and compare each's operating returns separately from their returns from leverage. There are quoted statistics on many sites for the 'Return On Equity' and 'Return on Capital Employed' and 'Debt To Equity'.

Plugging the metrics into the format, and solve for the interest rate being paid for the debt. Compare this rate between companies to see which company the lenders think is more risky. Compare the interest rate paid on debt against the company's ROE to see how close they are to experiencing the negative outcomes of leverage. If the debt's interest rate seems unreasonable it may be because the company is capitalizing interest payments. So check the disclosure of cash interest paid at the bottom of the Statement of Cash Flow.

Debt levels are discussed further on the Other Metrics page. Following that is a discussion of the ROIC metric (or Return on Assets).

EXAMPLE using 2004 StatsCan overall market data for ROCE, ROE and D/E
8% Operating Return (ROCE)
12.5% Leveraged Return (ROE)
1.094 Debt to Equity (D/E)

LONG-FORM MATH
Operating return (ROCE)1094+1000* 8%=167.52
less Debt interest (solve for) (1094)* 3.9%(=42.52)
equals Leveraged return (ROE)1000 *12.5%=12.5


#3 LEVERAGE WITH SPLIT-SHARE CORPS Top


There are so many split-share corp's in Canada that they deserve some analysis of their own. The market for these products is full of inefficiencies (ie. mispricing). Ownership is mainly by us Retail Investors. We don't do the necessary homework, and presume we are smarter than we actually are. The institutional players cannot get their required liquidity, so they aren't involved and don't keep the valuations 'correct'. Therefor these vehicles are a great place for smart investors to find bargains.

What is a split-share corporations? These listed companies have no active business of their own. They own a portfolio of public company shares or sometimes the shares of only one particular company, and layer their own corporate structure on top of it. The point of this structure is to satisfy demand from investors who want ONLY interest income, or only capital gains, or only dividends, or only taxable income, or only non-taxable income.

The assets are funded by a combination of preferred and common shares. And the income and gains from the portfolio are split between the two. When describing these companies, the media frequently claim that all the dividend income of the portfolio gets paid to the preferred shares. This is not true. Most frequently the preferred are paid a specified percent and the common shares get the rest. The actual income earned by the portfolio is irrelevant.

Because the debt is held within the corporation, it feels 'sanitized'. But equity owners must realize their returns will be exactly the same as if they had borrowed that money personally to buy the underlying assets. Added leverage always increases risk. Start by reading the Prospectus. Not the company's promotion - the real thing !!! You need to find out:

  • The ratio of preferred shares to common shares that make up one 'unit'.
  • The book value of the preferred shares (debt), and their redemption values at any different times.
  • The dividend payable to the preferred shares.
  • The payments to the common shares. Are they a set dollar amount or fluctuating with income? Will they deplete the assets?
  • If the company can call in either of the shares. At what time? At what price?
  • The total administration and overhead costs of running the product.
  • The ability of owners to retract their shares - give back to the issuer for cash.

You must also research the underlying investment. Does its dividend cover the payments to the split corp's Pfd Shares? Does its expected total return easily exceed the HURDLE RATE of the Pfd shares?

I will use the Sixty Split (T-SXT) as an example, but most are very similar. There are two equity shares plus one pfd share making up one unit. The pfd share was issued for, and is currently redeemable at $25.00. The fact that its market value is $25.80 is irrelevant to the equity owner. It only indicates that the owners are ignorant of the fact the pfd's are now callable: that they will lose (25.8/25.0 - 1=) 3.2% if called. Assume the underlying assets will earn 10%.

NAV of underlying asset$55.54* 10% = $5.554
less 5.7% Pfd share dividend ($25.00)* 5.7%= ($1.425)
= Two Equity Shares (Total)$30.54 * 13.5%= $4.129

Also Consider

  • your other borrowing opportunities. If the interest rate on the Preferred Share (5.7%) is higher than the rate you could borrow personally there is no point to the vehicle. But alternately, often these structured products have the ability to borrow at much lower costs than you can.
  • the tax savings from the deductibility of interest. If you borrowed personally at 5.7% you could recover (say) 45% on your tax return. The net cost of borrowing personally would be only 3.1% (5.7*(1-.45))
  • whether the borrowing is in Cdn or US dollars. US$ borrowings may hedge your currency exposure more simply than you can accomplish elsewhere.
  • The true 'hurdle rate' is greater than 5.7% because it is the equity shareowners who cover the costs of administrative overhead. These are 'fixed' costs that act just like fixed interest payments.

Short-form Calculation. Transform published leverage factor (Total Invested/Equity = 1.82) into Debt/Equity = .82.

Debt to Equity Multiple
.82
Interest Rate Differential(10 - 5.7)4.3%
Multiply Line1 * Line2
= 3.5%
Add Investment Return
+ 10%
Equals Total Return
= 13.5%


#4 LEVERAGE WITH OPTIONS Top

You can buy call options as a vehicle to leverage your returns, instead of just owning the stock outright. Not all options can be used to this purpose. You must find the right stock, the right strike price, calculate your total finance % and compare that rate to the cost of alternate sources of borrowing. This model for using options assumes you are NOT buying the option as a 'bet': that you want the exact same risk exposure as owning the stock.

There are two benefits to this use of leverage.

  • The 'hurdle' rate will be very low: essentially the T-bill rate - probably lower than you can borrow yourself.
  • The 'debt' (the strike price) is fundamentally denominated in the currency of the company itself. You can use this method to hedge currency risk on this portion.

Instead of owning and paying for the stock outright, you

  • Pay only a portion of the stock price (the intrinsic value of the option).
  • Pay interest on the remaining portion.
  • Invest that remaining portion in an alternate investment earning a higher return.
  • Realize that you lose the dividends paid to owners of the stock.

Your first step is to determine the interest rate you will be paying on that financed portion. This is detailed on a separate page.

Then you decide where to invest that financed portion.

  1. You can buy t-bills. Your returns will be the same as if you had bought and paid for the stock itself, with the same risk.

  2. You can create a 'carry trade' by investing in debt with a higher yield (watch out for assuming risk). The positive interest differential is ADDED to the return on the stock.

    In this example the underlying stock is assumed to grow at 8%. The option on that stock has an implicit 4% financing cost. The intrinsic value of the option premium is 15% of the stock price. So 85% of the purchase is financed. That same 85% is used to purchase debt earning 5%. The interest differential of 1% (=5-4) time leverage .85 (=85/100) plus stock return 8% equals 8.85%.

    Underlying Stock$100* say 8%= 8.0
    less Option Cost (85)* Implicit 4%(= 3.4)
    add Alt. Investment85* safe 5%= 4.25
    Equals Cash Investment100 * 8.85%= 8.85

  3. For maximum leverage and risk you can invest ALL your cash in the option premium. The interest differential (8-4 =) 4% times the leverage ratio (85/15 =) 5.67 plus the stock's return of 8% equals 30.7%

    Stock$100* say 8%= 8.0
    less Option Interest (85)* T-bill 4%(= 3.4)
    Equals Option Premium Paid15 * 30.7%= 4.6


#5 LEVERAGE WITH FUTURES CONTRACTS Top

Pricing a futures contract starts with the current value of the underlying security. With financial products there are two adjustment necessary. First consider that any dividends earned by the asset are NOT earned on the futures contract, so you would value it less, by the amount of the dividends missed. Then consider the 'time-value-of-money'. You have ownership exposure to the underlying asset right from the start, but you don't have to pay for it until the contract closes. You could have accomplished the same thing by borrowing money and buying it outright. Therefore you are willing to pay more for the futures contract equal to the interest you would have paid on that borrowing.

Consider the S&P 500 Index and the one-year futures contract on it.

  • The S&P Index itself = $1,504.66
  • less the dividends missed ( 1.93% $1,504.66 =) $29.04.
  • plus the interest you would have paid = $66.38 or 4.4% of the index value
  • equals the value of the futures contract = $1,542.

There is a helpful website that calculates at each day's end, the net effects of dividends and interest for each maturity of the S&P 500 and Dow Industrial index futures. See IndexArb.

When evaluating the interest implicit in the Futures contract remember that the interest you would pay on personal borrowings would be tax deductible at your full rate, while the futures contract will be taxed as capital gains. At a 40% tax bracket, that 4.4% rate in the Futures contract would equal 5.88% personal debt.

It is hard to quantify the leverage in a Futures contract. You must provide your broker with collateral, but that can stay invested in whatever else you are interested in. It is not a downpayment. You do not have to put any cash 'down', so leverage is 100% at the start. You DO have to come up with cash to cover any loss in value of the contract at the end of each day though. On the flipside, any increase in the contract's value results in cash being put INTO your account each day. So how much cash you put into the position over its life depends on the position's gains/losses.

Other factors can go into the pricing of a futures contract. Contracts for oil include the cost of storing the commodity. Foreign exchange contracts may include predicted changes in the Bank Rate. Contracts on the price of real estate include predictions of the future value of the underlying asset. From one POV all of these factors should be considered 'interest'. In all cases the futures contract can be duplicated by doing the deal today and paying for it with debt.

Leverage is not an unavoidable attribute of futures contracts, though. If you buy a T-bill with the cash that was NOT put down to buy the index future, you end up in the same position as someone buying the index for cash. If you buy a T-bill with the cash that was NOT put down to buy a currency future, you end up in the same position as someone who actually exchanges their currency at the start. Zero leverage.


#6 LEVERAGE WITH SHORTED STOCKS Top

The leverage effects of shorting are similar to those in futures contracts. At the start, the investment is 100% levered because there is no cash put down. Similarly with futures, over time cash is pulled out of your account if the position loses value, and deposited into your account if the position gains. So the debt/equity leverage ratio is dependant on the realized gain or losses. (The original proceeds from the short sale are usually not available for use, nor do they earn interest.)

In addition, you must compensate the true owner of the security for the interest or dividend income he should be receiving. Conceptually you can considered these amounts (as a percent) to be the hurdle rate of the leverage debt. Alternately they can be considered just part of the investment's total return, like dividends are just part of the long investor's total return. Theoretically when a company pays a dividend, its stock value declines by the same amount. The short seller would have to pay that dividend, but would also benefit from the decline in the stock.

Considered this way, shorting stock is the cheapest form of leverage. The effective interest rate is zero percent at the start. If the position is successful, the cash added to your account can be used for additional investments, creating a negative interest rate.

Shorting stocks does not necessarily mean you are negative on the market. You can short the ETFs that are themselves shorting the market (e.g. ProShares). A short of a short equals a long position. The issue of distributions complicates this strategy. There are commonly cash distributions made to both investors in an base index AND to investors in short ETFs. When shorting the short ETFs, you forgo the distribution long investors would get AND you must make good the distribution paid by short ETFs.

Like for futures, leverage is not an unavoidable attribute of shorting.


#7 LEVERAGE WITHIN OPERATIONS Top

Business's cost of production can be either fixed or variable. Variable costs increase proportionally with increases in revenue. They create no leverage. Think of the variable labour costs of a tech company. Hires and layoffs keep costs in proportion to revenues.

Fixed costs stay the same when revenues increase. Any increase in revenues falls straight to the bottom line, magnifying gains. The interest on debt is a fixed cost. The effect of different capital structures was shown at the top of this page. But other costs are fixed. Businesses with large infrastructures like mines have costs that were determined when the mine was dug. Any increase in the commodity price creates a magnified increase to profits.

This chart shows the effect of a 20% increase to revenues. The first company has variable costs equal to 60% of revenues. The second company has $60 fixed costs. The increase to the bottom line is levered with fixed costs.


Variable Cost CoFixed Cost Co

Start...Incr 20%Start...Incr 20%
Revenues $100$120$100$120
less Costs $ 60$ 72$ 60$ 60
equals Profits $ 40$ 48$ 40$ 60
Increase in profits
20%
50%

Of course companies do not disclose whether their costs are fixed or variable. It can only be surmised from their historical financials and your understanding of the business.

Next consider the leverage differences between companies both of which have fixed costs. Here we see that the low-cost producer has less leverage than the high-cost producer. This is counter-intuitive. Most investors would think it smarter to buy the company with the 'best' cost structure. But when you are gambling on an increase to revenues for all competitors, your returns will be larger with the 'worst' company.


Low Cost CoHigh Cost Co

Start...Incr 20%Start...Incr 20%
Revenues $100$120$100$120
less Costs $ 40$ 40$ 60$ 60
equals Profits $ 60$ 80$ 40$ 60
Increase in profits
33.3%
50%


#8 ACADEMIC PAPER Top

An interesting paper on the optimum level of leverage for Canadian portfolio investors is at Long Run Effects of Risk.