Rule 7

[Clive]

...

[hoost]

Based on what I've read and heard from HB, I think the idea wasn't so much optimizing gains but limiting losses.  When he talks about speculating with the VP, this is what he focuses most on.  In general the principle seems to be, don't put yourself in a situation where you can lose more than you've put in; if you stick to that, even if you take a loss on a trade it's unlikely to be catastrophic.

[Gosso]

Hmmm, well I checked out the Canadian leveraged ETF's and they do not look healthy (LINK):

HXU = Bull x2     HXD = Bear x2     TSX = TSX 60 index

Code: Select all

 	1 mo	3 mo	6 mo	YTD	1 yr	3 yr	5 yr	SIR *
HXU	-3.0 %	8.1 %	11.9 %	8.1 %	-26.8 %	19.4 %	-12.6 %	-6.2 %
HXD	2.3 %	-9.1 %	-17.2 %	-9.1 %	16.2 %	-28.4 %	-26.2 %	-17.1 %
TSX	-1.3 %	4.6 %	7.5 %	4.6 %	-10.2 %	13.2 %	2.4 %	2.2 %
* performance since inception on January 8, 2007.

They have a MER of 1.15%, and a massive tracking error.  I'll pass.  :)

As for using margin, I'm not sure.  I have thought a lot about it, but figured it wasn't worth it.  My broker charges 4.25% on margin, but I can write the interest off on my taxes, so lets say it is now 3.5%.  Also throw in inflation of 2%, and that means the margin is costing me a real interest rate of 1.5%.  That means I need to achieve a real rate of return of at least 1.5% on my investments.  You would think this would be okay for the PP, but based on the chart below, it doesn't seem to work very well.  It appears to be almost a wash, and is dependent on when you began using the margin.

Code: Select all

     Nominal	Prime	Diff	 Value 		       Prime	Diff	   Value 
       Gain 	Rate		of $100,000		Rate 		  of $100,000
      (CA PP)                      Margin              (+1.5%)            Margin
1970	4.8	7.5	-2.7	 $97,275.00 		9.0	-4.2	 $95,775.00 
1971	10.5	6.0	4.5	 $101,635.83 		7.5	3.0	 $98,631.96 
1972	20.8	6.0	14.8	 $116,634.50 		7.5	13.3	 $111,707.86 
1973	21.8	9.5	12.3	 $130,936.73 		11.0	10.8	 $123,730.35 
1974	12.2	11.0	1.2	 $132,540.71 		12.5	-0.3	 $123,390.09 
1975	3.1	9.8	-6.7	 $123,660.48 		11.3	-8.2	 $113,272.10 
1976	10.9	9.3	1.6	 $125,652.01 		10.8	0.1	 $113,397.25 
1977	13.1	8.3	4.9	 $131,807.89 		9.8	3.4	 $117,251.79 
1978	20.9	11.5	9.4	 $144,184.09 		13.0	7.9	 $126,502.46 
1979	44.4	15.0	29.4	 $186,584.98 		16.5	27.9	 $161,806.09 
1980	14.8	18.3	-3.5	 $180,101.15 		19.8	-5.0	 $153,756.24 
1981	-9.9	17.3	-27.1	 $131,242.96 		18.8	-28.6	 $109,738.60 
1982	24.5	12.5	12.0	 $147,054.51 		14.0	10.5	 $121,313.32 
1983	12.8	11.0	1.8	 $149,732.29 		12.5	0.3	 $121,702.68 
1984	3.3	11.3	-7.9	 $137,828.57 		12.8	-9.4	 $110,201.77 
1985	20.1	10.0	10.1	 $151,692.22 		11.5	8.6	 $119,633.52 
1986	14.2	9.8	4.4	 $158,389.78 		11.3	2.9	 $123,121.11 
1987	6.8	9.8	-3.0	 $153,703.44 		11.3	-4.5	 $117,631.47 
1988	3.2	12.3	-9.1	 $139,735.73 		13.8	-10.6	 $105,177.30 
1989	12.0	13.5	-1.5	 $137,625.90 		15.0	-3.0	 $102,011.60 
1990	-0.3	12.8	-13.1	 $119,665.72 		14.3	-14.6	 $87,168.91 
1991	11.6	8.0	3.6	 $123,930.30 		9.5	2.1	 $88,967.85 
1992	6.4	7.3	-0.9	 $122,829.17 		8.8	-2.4	 $86,842.85 
1993	21.6	5.5	16.1	 $142,598.47 		7.0	14.6	 $99,517.52 
1994	-1.9	8.0	-9.9	 $128,523.93 		9.5	-11.4	 $88,202.33 
1995	14.9	7.5	7.4	 $138,010.17 		9.0	5.9	 $93,389.44 
1996	13.1	4.8	8.3	 $149,496.91 		6.3	6.8	 $99,761.50 
1997	5.1	6.0	-0.9	 $148,151.44 		7.5	-2.4	 $97,367.23 
1998	6.1	6.8	-0.7	 $147,145.43 		8.3	-2.2	 $95,245.55 
1999	5.8	6.5	-0.7	 $146,154.03 		8.0	-2.2	 $93,175.15 
2000	7.5	7.5	0.0	 $146,113.80 		9.0	-1.5	 $91,751.88 
2001	1.1	4.0	-2.9	 $141,947.54 		5.5	-4.4	 $87,759.40 
2002	5.7	4.5	1.2	 $143,617.99 		6.0	-0.3	 $87,475.77 
2003	9.9	4.5	5.4	 $151,375.15 		6.0	3.9	 $90,888.42 
2004	7.7	4.3	3.4	 $156,590.63 		5.8	1.9	 $92,656.56 
2005	13.8	5.0	8.8	 $170,436.93 		6.5	7.3	 $99,459.73 
2006	11.2	6.0	5.2	 $179,282.11 		7.5	3.7	 $103,129.51 
2007	7.2	6.0	1.2	 $181,361.55 		7.5	-0.3	 $102,778.73 
2008	-3.0	3.5	-6.5	 $169,605.16 		5.0	-8.0	 $94,574.63 
2009	12.5	2.3	10.3	 $187,059.37 		3.8	8.8	 $102,888.77 
2010	14.3	3.0	11.3	 $208,255.21 		4.5	9.8	 $113,003.84 
								
AVG	10.6	8.4	2.2	                       	9.9	0.7	  

Prime rate data: http://www.bankofcanada.ca/wp-content/u ... _50_51.pdf

So in my mind it is not worth the extra risk to potentially juice the returns a bit.  Basically all you are doing is placing a bet against the bank that they are not charging enough on their prime rate.

Once again, HB was right.

Edit: Fix column headings

[Gosso]

Holy Shit, your right!  I just made a simple portfolio with 50% HXU and 50% XSB (short term Canadian bonds), and it seems to match the TSX very well.  Plus I didn't even factor in re-balancing.



But this doesn't make any sense.  There has to be some sort of voodoo going on here...where is the decay and cost to borrow?

Also it doesn't appear that HXU pays dividends, do the dividends pay for the leverage costs?  Or is the cash supposed to compensate for the lack of dividends?

[Gosso]

Clive, very interesting...you have sparked my interest in these leveraged ETF's, and I will continue to research them.  But I have a suspicion that this is too good to be true...it just feels like a free lunch.

Here are a few questions:

-  Are all the borrowing costs contained within the ETF's MER?  It seems impossible that they can cover their costs, make a profit, and pay for leverage with only 1.15% -- they must be building these with derivatives and futures.  I guess what I'm saying is that there must be plenty of counter-party risk to achieve such a low borrowing cost.

- Besides a one day drop of 33% (or 50% in the case of x2), what else could make these blow-up?  They did survive 2008 well enough, so it seems they can handle a lot.

- If the company or ETF goes bust, what are you left with?  A bunch of future contracts?  Or nothing?

I'm going to need to comb through the prospectus, to get a feel for how these are built.

[Gosso]

More likely leveraged funds will be holding a combination of 1x underlying and also be using derivatives. The time value (cost to borrow) for derivatives is typically similar to short term treasury yields. Those trading/borrowing costs would typically be absorbed from the fund value, not from the expense ratio, so the daily price of the fund reflect those costs having been absorbed. Although with higher expense ratio's, perhaps they proportion the costs to a bit of both expenses and from fund value.

It would then appear that anyone using a margin account at 4.25% is a complete sucker, especially when options/futures/derivatives can be leveraged for basically 0-1%.

So we can expect that x2,3 ETF's will see a higher "slippage" when/if interest rates and therefore borrowing costs increase.  Or if inflation/deflation drops below the rate of borrowing...?

If a Canadian holds 8.3% in each of US 3x stocks (BGU), 3x LTT (TMF), 3x Gold (UGLD) and 75% in Canadian short term treasury then they're exposed to

25% Stock
25% LTT
25% Gold
25% USD
75% CAD
75% lent (buy STT)
50% borrowed (via ETF's)

For the 75% CAD exposure, that risk is reduced by also holding 25% gold and 25% USD - to a 25% overall type amount.
75% lent and 50% borrowed is a net 25% lending overall amount.
There's also carry-trade positions in that (USD versus CAD interest rate differentials).

There's more asset classes to measure - and perhaps periodically rebalance (add-low/reduce-high).

Whilst that starts of relatively simple, after rebalancing - for instance to perhaps reduce USD, add to CAD so as to realign overall to 25% CAD exposure - you'll end up with a more mixed bag of USD and CAD holdings. So there will be more holdings/more rebalancing /more trading costs. That might however generate more rewards.

Interesting, very very interesting.  But based on my backtesting, I have seen that a US PP held by a Canadian can be quite volitile and has had a much lower return over the past 30 years (basically due to the fluctuations in the USD/CAD).  I would prefer to use mostly CAD assets, but unfortunately there is not a leveraged CAD LTT.  I suppose I could buy the real futures, but I have a lot of homework ahead of me before I dive into that.  I know very little about how the options/futures markets work.

[Gosso]

So we can expect that x2,3 ETF's will see a higher "slippage" when/if interest rates and therefore borrowing costs increase?

No - because the 'cash' you hold also rises/falls in reflection.

$100 total, you invest $50 in 2x, $50 in 'cash'.
2x ETF takes your $50, borrows another $50 at 'cash' rate and invests $100 in the 1x underlying stock.

If the cost of borrowing increases and the fund pays more for the $50 they borrow, you'll also receive more for the $50 in cash that you hold.

That makes sense.

I came across this in my reading on options, which sounds very similar to what you are suggesting, except with options:

II. Buying Calls as part of an investment plan 

A popular use of options known as "the 90/10 strategy" involves placing 10% of your investment funds in long (purchased) calls and the other 90% in a money market instrument (in our examples we use T-bills) held until the option's expiration. This strategy provides both leverage (from the options) and limited risk (from the T-bills), allowing the investor to benefit from a favorable stock price move while limiting the downside risk to the call premium minus any interest earned on the T-bills. 

Assume XYZ is trading at $60 per share. To purchase 100 shares of XYZ would require an investment of $6,000, all of which would be exposed to the risk of a price decline. To employ the 90/10 strategy, you would buy a six-month XYZ 60 call. Assuming a premium of 6, the cost of the option would be $600. This purchase leaves you with $5,400 to invest in T-bills for six months. Assuming an interest rate of 10% and that the T-bill is held until maturity, the $5,400 would earn interest of $270 over the six month period. The interest earned would effectively reduce the cost of the option to $330 ($600 premium minus $270 interest). 

If the price of XYZ rises by more than $3.30 per share, your long call will realize the dollar appreciation at expiration of a long position in 100 shares of XYZ stock but with less capital invested in the option than would have been invested in the 100 shares of stock. As a result, you will realize a higher return on your capital with the option than with the stock.

If the stock price instead increases by less than $3.30 or falls, your loss will be limited to the price you paid for the option ($600) and this loss will be at least partially offset by the earned interest on your T-bill plus the premium you receive from closing out your position by selling the option, if you choose to do so.

Source: https://swww.scotiaitrade.com/html/cust ... tml#bcalls

Although I'm thinking you have more creative methods for utilizing the cash. 

Can you think of any potential problems with using options instead of leveraged ETF's.  Obviously options use much more leverage and can easily become worthless, but this can be compensated by leveraging only ~10% of the portfolio, rather than 50% as for the x2 ETF's.

Side Bar: Apparently there are no options or leveraged ETF's for Long Term Canadian Bonds.  If I ever do this, I'll have to use options on TLT/EDV or leveraged US ETF's.

[clacy]

So we can expect that x2,3 ETF's will see a higher "slippage" when/if interest rates and therefore borrowing costs increase?

No - because the 'cash' you hold also rises/falls in reflection.

$100 total, you invest $50 in 2x, $50 in 'cash'.
2x ETF takes your $50, borrows another $50 at 'cash' rate and invests $100 in the 1x underlying stock.

If the cost of borrowing increases and the fund pays more for the $50 they borrow, you'll also receive more for the $50 in cash that you hold.

That makes sense.

I came across this in my reading on options, which sounds very similar to what you are suggesting, except with options:

II. Buying Calls as part of an investment plan 

A popular use of options known as "the 90/10 strategy" involves placing 10% of your investment funds in long (purchased) calls and the other 90% in a money market instrument (in our examples we use T-bills) held until the option's expiration. This strategy provides both leverage (from the options) and limited risk (from the T-bills), allowing the investor to benefit from a favorable stock price move while limiting the downside risk to the call premium minus any interest earned on the T-bills. 

Assume XYZ is trading at $60 per share. To purchase 100 shares of XYZ would require an investment of $6,000, all of which would be exposed to the risk of a price decline. To employ the 90/10 strategy, you would buy a six-month XYZ 60 call. Assuming a premium of 6, the cost of the option would be $600. This purchase leaves you with $5,400 to invest in T-bills for six months. Assuming an interest rate of 10% and that the T-bill is held until maturity, the $5,400 would earn interest of $270 over the six month period. The interest earned would effectively reduce the cost of the option to $330 ($600 premium minus $270 interest). 

If the price of XYZ rises by more than $3.30 per share, your long call will realize the dollar appreciation at expiration of a long position in 100 shares of XYZ stock but with less capital invested in the option than would have been invested in the 100 shares of stock. As a result, you will realize a higher return on your capital with the option than with the stock.

If the stock price instead increases by less than $3.30 or falls, your loss will be limited to the price you paid for the option ($600) and this loss will be at least partially offset by the earned interest on your T-bill plus the premium you receive from closing out your position by selling the option, if you choose to do so.

Source: https://swww.scotiaitrade.com/html/cust ... tml#bcalls

Although I'm thinking you have more creative methods for utilizing the cash. 

Can you think of any potential problems with using options instead of leveraged ETF's.  Obviously options use much more leverage and can easily become worthless, but this can be compensated by leveraging only ~10% of the portfolio, rather than 50% as for the x2 ETF's.

Side Bar: Apparently there are no options or leveraged ETF's for Long Term Canadian Bonds.  If I ever do this, I'll have to use options on TLT/EDV or leveraged US ETF's.

It seems that a Canadian investor could easily compensate for the currency risk with a small amount of money in FX or options on the US or Canadian dollar if you employed this strategy (investing in US based leveraged trading vehicles).

[Gosso]

It seems that a Canadian investor could easily compensate for the currency risk with a small amount of money in FX or options on the US or Canadian dollar if you employed this strategy (investing in US based leveraged trading vehicles).

You are right, but it may not be worth it.  iShares Canada will typically hedge their international ETF's against the USD/CAD fluctuations, but the hedging increases the tracking error by about 1%.  :o  So if iShares cannot figure it out, then I'm probably screwed.  Plus if I simply setup the portfolio to embrace the volatility between the CAD/USD then I should be in better shape.  I have some ideas on how to do this, likely 50% CAD / 50% USD and Gold.

It also appears that Canadian Options are not an option feasible due to literally no volume and massive spreads.

***

I had a tough time wrapping my brain around how the 2x DAILY movement on the leveraged ETF's worked, so I used the random number generator to create a pseudo-leveraged index.  I had previously thought that if the index dropped 50% over a period of time then the x2 ETF would be zero, but this shows that assumption was incorrect.



They seem to be fairly resilient, although I didn't factor in the 1% MER, cost of leverage, or other potential tracking errors.

[Tortoise]

I had a tough time wrapping my brain around how the 2x DAILY movement on the leveraged ETF's worked, so I used the random number generator to create a pseudo-leveraged index.  I had previously thought that if the index dropped 50% over a period of time then the x2 ETF would be zero, but this shows that assumption was incorrect.

Cool stuff. From your plots, it looks like if the 1x curve has changed by a factor of (1+x) over a period of time (where x is greater than or equal to -1.0), the 2x curve has changed by a factor (1+x)2, the 3x curve has changed by (1+x)3, and so on.

That actually makes sense if you think about it. For example, the cumulative price change for 2x daily movements of x1, x2, x3, etc. is (1+2x1)(1+2x2)(1+2x3)... And since (1+2x) is a close approximation of (1+x)2 for small values of x, the cumulative price change is approximately (1+x1)2(1+x2)2(1+x3)2... But that just equals [(1+x1)(1+x2)(1+x3)...]2..., which is the square of the 1x price change. Similar reasoning applies for 3x, 4x, etc.

Bottom line: I think the reason that leveraging the daily movements, x, by some factor N results in curves that look like the ones you plotted is because (1+Nx) closely approximates (1+x)N for small values of x. (Daily price movements do tend to be small.)

[EDIT: The approximation above applies mainly to Gosso's top two plots, where the price movements all tend to be in the same direction. In the bottom two plots, the up-and-down movements create volatility drag, which invalidates the approximation.]

[Gosso]

Tortoise,

I compared (1+2x) to (1+x)2 in Excel, and you are correct (not that I doubted you ).  But, as you said, once you step outside of +/-1% daily moves then the (1+x)2 seems to slightly outperform (1+2x) during bull, bear, and flat markets.  The greater the volatility, the greater the difference.

[EDIT: The approximation above applies mainly to Gosso's top two plots, where the price movements all tend to be in the same direction. In the bottom two plots, the up-and-down movements create volatility drag, which invalidates the approximation.]

Regarding volatility drag, it seems the leveraged ETF will over come this once the underlying index makes a decent move higher, as can be seen in the bottom right chart.  Although I haven't factored in the cost to borrow or the higher MER.

After each decline in the 1x, a 2x holds less leverage the next day. After each rise in the 1x, the 2x holds more leverage the next day. That puts a brake on declines and amplifies upsides, that your charts show.

In the top left chart, after the 1x had declined around -50%, the 2x was down around -75% (approximating by eye). In the top right chart, after the 1x had risen +50%, the 2x was up around 125%.

Holding half in the 2x as a synthetic 1x might see (respectively) +62.5% versus +50% on the upsides and -37.5% versus -50% on the downsides. i.e. half in the 2x is potentially better than holding the 1x.

So what you're telling me is that 'Free Lunches' do exist!  "Please sir I want some more", "No problem, here you go." 

Although the higher MER and cost to borrow will dampen the difference somewhat...but then again the cash component may compensate for this to a certain degree.

[craigr]

Ok, I'll be the wet blanket. 

I have never seen any leveraged strategy work well long term. Risks are always there, even if unseen at first.

[craigr]

It's about sleeping well at night for me. I never want to wake up in the morning and read the news to find out that my leveraged position has completely blown up due to some unforseen risk. I know plenty of people that got either completely, or nearly, wiped out using leverage. I avoid it at all costs and at all times in my investing portfolio. I just don't see the benefit to using it compared to the risks of what happens if it goes the wrong way.

[FarmerD]

Nice charts Gosso

After each decline in the 1x, a 2x holds less leverage the next day. After each rise in the 1x, the 2x holds more leverage the next day. That puts a brake on declines and amplifies upsides, that your charts show.

In the top left chart, after the 1x had declined around -50%, the 2x was down around -75% (approximating by eye). In the top right chart, after the 1x had risen +50%, the 2x was up around 125%.

Holding half in the 2x as a synthetic 1x might see (respectively) +62.5% versus +50% on the upsides and -37.5% versus -50% on the downsides. i.e. half in the 2x is potentially better than holding the 1x.

Since the individual components of the PP are so volatile, this is why my backtested hypothetical 2x PP did so well.  This topic is fascinating since only the component assets in the pp would seem to allow this strategy to work.  Any other 2x strategy would necessarily be using assets that are more correlated leading to highly volatile yearly returns. 

[FarmerD]

In case anyone is interested, here are my yearly results for a hypothetical 2x portfolio of gold, TSM, LTT.  I adjusted the returns of each of the components each year using an average volatility of 25%.  The results show less volatility than the TSM (TSM had 10 losing years, the 2x had 7 losses) The 3x simulation backtest produced a slightly higher CAGR but also far more volatility and endured a 22 year period of underperformance relative to the standard PP.  I think Clive has pointed out the 2x seems to apply the optimal amount of leverage and based on my results, that seems right. 


45.3
47.3
41.3
16.3
21.7
7.7
25.0
149.3
22.0
-24.0
46.3
1.3
-2.3
44.7
37.3
7.3
3.3
26.0
-7.3
25.0
-0.3
24.0
-11.7
38.0
5.0
14.0
18.7
5.0
-2.0
-9.7
8.2
29.7
9.9
12.9
20.6
24.6
1.2
8.0
31.5
25.8

Cagr: 16.80%