# I just invested an equation

Discussion in 'Investing Strategies' started by -T-, 23rd Apr, 2006.

1. ### -T-Well-Known Member

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Ok, maybe I'm not the first, but it was a revelation nonetheless. Actually, since this forum is full of finance types, I wouldn't be surprised if I'm actually the last person to work this out. Anyway, I wanted an equation to show return when considering leverage. For example 10% on a 500000 house geared to 80% isn't really a return of 10%, it's more like 50%.

The reason this is of interest is because I'm writing my investment strategy and trying to work out my next investments. I started to wonder when a lower return at higher leverage outweighs a higher return at lower leverage.

So, the equation is:

(1 + return)^term - 1
---------------------
1 - gearing

It gives the real rate of return when giving the nominal rate of return, the rate of gearing and the term in years (or periods if the rate of return is per period). I thought it may be of use to someone else.

I think it works fine, I tested it, I hope it works

2. ### -T-Well-Known Member

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I have attached a spreadsheet that tables and graphs comparisons. This was actually really interesting for me to see.

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3. ### johnnybWell-Known Member

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Hi -T-,

Can you explain where the "-1" in the numerator comes from. My understanding is that the total return is simply given by

(1 + return)^term
-----------------
1 - gearing

As I think we all know, compounding is magic, which is why time is so important in investing. As you have found, the case with higher return and lower gearing will always (eventually) win over the low return but high gearing case.

John.

4. ### Nigel WardTeam InvestEd

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10th Jun, 2005
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1,172
Mr T

That's a nice lookin spreadsheet! I must be a bit simple though. Using your example don't you just say:

1) 500k @ 80% gearing means \$100k equity
2) 10% return on \$500k = \$50k
3) 50/100 = 50% return on equity before int costs
4) say 7% interest only on \$400k borrowings equals \$28k
5) net return is \$22k
6) net ROE = 22%
7) maybe you add back tax benefit of int being deductible so say at top marginal rate you'd add back 28k x 48.5% = \$13,580
8) after tax benefits net ROE = \$35,580 thus 35.58% ROE

that's enough maths for one morning...

Cheers
N.

5. ### -T-Well-Known Member

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Hi John

The "-1" comes from me messing with the equation until it worked. But without the "-1" it simply doesn't work.

Say for:
Capital = 100k, return = 10%, leverage = 80%, 2 years

If you use (note: no "-1"):
(1 + return)^term
---------------------
1 - gearing

You get: 6.05

You definitely don't make 605k in 2 years with a 500k investment @ 10%.

Maybe we're talking about different things then.

6. ### johnnybWell-Known Member

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Yes, I think we're getting our definitions mixed up - I see what you're doing now. In this example, if you invest \$500K @ 10%, then after 2 years your total investment will be 605K. This is what I was calculating. Your return would be 105K, which on your initial 100K is a 105% return. Your original equation will give you 1.05, or 105%. I think we're on the same page now - I should have read your original post more closely .

John.

7. ### -T-Well-Known Member

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Hi Nigel

The idea simply started off only to compare leverage and return. I know there's a lot more to real return than just leverage, but the question I was asking myself had to do with the importance of leverage vs. return.

Like John said, the higher return will always eventually win, but 'eventually' can be a long time. So I wanted an equation that could differentiate two investments based on leverage and return. I just put investment capital in that spreadsheet for illustrative purposes.

Say that your outlook was long enough to not put any focus on market timing. So then say you wanted to compare buying a residential investment property to a top performing Asian equities fund. You have 100k to spend. For the sake of simplicity, the IP can be geared to 80%, the historic return on that IP is 10% and your outlook is 20 years. Say the fund is geared to 50%, a return of 18% with the same outlook. So which has the better return?

Like you showed, it's easy to work out the returns with a particular case. But what about when comparing asset classes or asset types. I wanted to understand why Michael Yardney says IPs are better because you get better leverage and why Spann says equities are better due to better return. Yardney actually says IPs are only the best investment because of the high leverage. But this formula shows that return is king in the long-term.

I know this is obvious stuff for some, but I've started to realise I have to reinvent every concept for myself. The books, the pros, the seminars all tend not to tell the real story. I think I mentioned in another thread that other than the simple concepts of leverage and compounding, I've almost proven every concept in the books I own wrong.

Some might say this in analysis paralysis, but you just have to look at that spreadsheet to see the differences in performance. You would still be successful just investing, but I'm talking about optimising your strategy to its greatest potential. I think Peter Spann was right in saying selection is 70% of success. Ok, I don't know where he got 70%, but I think it is very important.

8. ### -T-Well-Known Member

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Ahhh, I thought "605k, what sort of random number is that!" But of course it's the return not taking away the borrowed money. I'm so docile, hehe.

9. ### Nigel WardTeam InvestEd

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10th Jun, 2005
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1,172
Hi T

Sorry I wasn't trying to suggest your analysis wasn't important.

Like you, I find that I tend to need to arrive at a conclusion myself before I really believe it!

I had one of those "a hah" blinding flashes of the obvious the other day when lodging some additional shares as security for margin lender. Even though the performance of these small-mid caps has been good, they just won't lend as much against them. Which if you're gearing means you need a higher return from them...as your modelling shows.

Cheers
N.

10. ### -T-Well-Known Member

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Hi Nigel. I never took it that way, but I think my replies sometimes lack a bit of tact or consideration. I respect everything that is said here and you actually gave me the idea to incorporate transaction costs, tax concessions, etc into that spreadsheet. It may become a handy investment comparison calculator after all of that.

11. ### johnnybWell-Known Member

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Do you want to share some of the things that you have found are wrong?

John.

12. ### Ol School SkataWell-Known Member

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7th Nov, 2005
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Is this similar to a cash on cash return?

I think it is wise to consider your return on cash in any investment when reviewing or researching investments in conjunction with considering the risk side of things as well as overall performance

OSS

13. ### -T-Well-Known Member

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Hi John

There have been a few, but I haven't got my notes with me. I'm just expressing my opinion here and would be glad to be proven wrong. The concepts I disagree with that come to mind are:
1. CG + yield = constant
2. Commercial CG is lower than residential CG because commercial CG is purely based on yield growth (which is generally indexed to inflation)
3. Residential IPs are the most profitable investment due to available leverage
4. Buildings/fixtures/fittings only ever depreciate

There's more, but they are the ones I've talked about recently. I realise these findings aren't cataclysmic, but they have changed the way I view what the pros say.

-T-

14. ### -T-Well-Known Member

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Hi There

I have attached an updated spreadsheet. I added another worksheet that shows you the combination of gearing and return you need to provide a particular real return.

For example, if your strategy has a goal to reach \$x equity in three years, just type in the return on equity needed and the term and then it shows a table of possibilities.

In my strategy, I want to grow my equity by 100% in three years, so the possibilities are:
- 50% gearing @ ~14.5% return
- 60% gearing @ ~13% return
- 70% gearing @ ~10% return
- 80% gearing @ ~7% return
- 90% gearing @ ~4% return

NB: those returns aren't exact, they are just the y-axis values I inputted that match my requirements closer than the other values.

Anyway, check out the spreadsheet if interested. The second worksheet shows this stuff.

PS I just realised the title of this thread, I meant invented not invested. Anyway...

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