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Energetic
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Total Posts: 1414
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Posted: 2016-10-25 18:38
I saw a product that is advertised to work as follows.

They lock your capital for N years although you can withdraw 10% a year w/o a penalty. Then, every year your account is credited with "interest" computed as

MAX(0, index performance - margin)

The investor has several choices of major indexes. The margin, taking into account dividends, works out to about 4.5%. In other words, they seem to sell complete downside protection at the cost of 4.5% of annual return.

Rather than tying my money with a third party and carrying credit risk I'd rather replicate this product myself but I don't see how. For example, a 1 year ATMF put on SPY even in the current low vol environment costs over 7%.

Any thoughts?

For every complex problem there is an answer that is clear, simple and wrong. - H. L. Mencken

chiral3
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Posted: 2016-10-25 19:09
You've entered the world of Real World versus Risk Neutral. You must perform a mental change of measure and hold a ton of fixed assets on balanace sheet.

One more technicality - the premium is usually paid as a % of the guarantee. In "option speak" it is drawn on the steadily increasing K as opposed to S.

Nonius is Satoshi Nakamoto. 物の哀れ

Energetic
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Total Posts: 1414
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Posted: 2016-10-25 23:07
That turn was a little too hard for my horse. If I need to buy puts with increasing K, it only makes options more expensive. Still don't understand how to replicate it.

For every complex problem there is an answer that is clear, simple and wrong. - H. L. Mencken

chiral3
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Posted: 2016-10-25 23:48
You can replicate it with it with vanillas providing you aren't using risk neutral vols and rates. So if replication is simple Black-Scholes, i.e., the final PO is replicated by interest on the premium and G/L on delta hedging, assuming the r-q and sigma is realized. Also, when you sell many of these products, a certain number of contract holders will take before N. This assumption lowers the price too. I am guessing you're looking at a retail product with a guarantee sold as an investment or an insurance product.

Nonius is Satoshi Nakamoto. 物の哀れ

TakeItAndRun


Total Posts: 89
Joined: Apr 2010
 
Posted: 2016-10-26 11:46
To replicate this structured product:
Invest in a 10 year Us treasury note (current yield 1.76%).
Buy 1 year OTM call on S&P500 and 9 other forward start 1 year OTM calls on S&P500 for a total cost of 1.76% per year.

If you cannot buy forward start options, then buy a 10 year OTM call.
If you cannot buy a 10 year OTM call, then invest in the following portfolio: 10%+x% short term Us bonds , 90%-x% SPY where x% depends on your risk aversion.
I think the recommended long term portfolio by Buffet is 10% short term bonds, 90% SPY. In case of crash, sell bonds and buy SPY.




chiral3
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Posted: 2016-10-26 13:10
It's uncapped.

Nonius is Satoshi Nakamoto. 物の哀れ

Energetic
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Posted: 2016-10-26 19:00
Maybe I'm beginning to understand. What I think you're suggesting is that I have to buy puts based on the real-life prob of the market going down. That would bring up at least two problems: if my estimate of future prob distribution is off then I'm screwed and I'm not guaranteed to achieve the replication if I do it on my own. Even the insurer who operates a pool of policies risks a loss. Right?

Yes, it's a retail investment product.

For every complex problem there is an answer that is clear, simple and wrong. - H. L. Mencken

chiral3
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Posted: 2016-10-26 19:42
That's right. Although note they are capitalized at a very high level, even by non-risk-neutral standards.

In general the withdrawal goes against the index performance (S) and the fee comes out of the guarantee. Therefore the guarantee is less market sensitive.

One other way to think about it is it is all an assumption. If a MM really thinks one year vol is rich he can sell it and scalp the premia. If a fund thinks basket vol is richer than index vol he's free to short one and buy the other. They are all assumptions. 1Y SPX vol is 10 vols higher than realized for some time now. Of course the insurers are a little screwed because we haven't been realizing the forward rates, never mind having long-term equity growth rates of 9% (as is standard in institutional assumptions).

In capped versions where there are payouts during [0,N] one can think abut it as being replicated as a strip of fwd starts, although this product will not have the other bells and whistles and the method will often underprice the fwd skew (assuming convex vol).

Nonius is Satoshi Nakamoto. 物の哀れ

Energetic
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Posted: 2016-10-26 19:51
Thanks!

For every complex problem there is an answer that is clear, simple and wrong. - H. L. Mencken

chiral3
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Posted: 2016-10-26 20:06
It's an irony in the reinsurance market - private equity and hedge funds may love reinsurance premiums, as they are uncorrelated with their core business. However, when the demand is highest rates are normally low, and the cost is prohibitively high. As rates rise the price differentials normalize but the demand falls off.

Nonius is Satoshi Nakamoto. 物の哀れ

TakeItAndRun


Total Posts: 89
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Posted: 2016-10-26 22:42
@chiral3:"It's uncapped."
The payoff of an OTM call is also uncapped.

Energetic
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Total Posts: 1414
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Posted: 2016-10-28 15:48
@TakeItAndRun

How do I get downside protection?

For every complex problem there is an answer that is clear, simple and wrong. - H. L. Mencken

TakeItAndRun


Total Posts: 89
Joined: Apr 2010
 
Posted: 2016-10-28 23:45
Let's take the first replication (long 10-year us treasury, long 1 1-year OTM call, long 1 1-year OTM call starting in 1 year, long 1 1-year OTM call starting in 2 years, long 1 1-year OTM call starting in 3 years....
Let's call IndexN the index price after N years.

At the end of the first year:
one receives 1.76% as bond coupon
one pays 1.76% for the OTM call
the OTM call delivers its payoff Max(0, index performance - strike in %) where index performance is (index1 - index0) / index0

At the end of the second year:
one receives 1.76% as bond coupon
one pays 1.76% for the OTM call
the OTM call delivers its payoff Max(0, index performance - strike in %) where index performance is (index2 - index1) / index1
...
Hence the protection is the fact one buys calls which are financed by bond coupons.

Let's take the last replication with 80% bond/20% SPY:
Invest 80% in a 10 year bond
Invest 20% in SPY

After 10 years, you get 80% from principal + 0.8 x 17.6% from coupons + interest from coupons and dividends + 0.2 x dividends from SPY + 0.2 x SPY10

Assuming a 2% dividend yield, it means (rough calculation):
80% + 14.08% + epsilon + 0.2 x 10 x 2% + 0.2 x SPY10
or 98.08% + epsilon + 0.2 x SPY10

In this case, after 10 years, one gets almost 100% in cash and 20% of a risky asset hence the protection.

Energetic
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Posted: 2016-10-31 16:57
Thank you, understood the protection but not the upside.
1. Won't work b/c even if I could obtain those fwd starting calls, 1.76% premium will only pay for the strike that is very likely to expire worthless. E.g. today, a one year out call with this premium buys ~15% OTM call. Quite possible that all (certainly most of) these calls will expire worthless and you will realize little if any upside.
2. You get 20% of upside with your strategy, not compounded (index-4.5%)+

For every complex problem there is an answer that is clear, simple and wrong. - H. L. Mencken

sigma


Total Posts: 105
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Posted: 2016-11-24 12:44
Using forward start calls, which are OTC, gives you the exposure to the counterparty risk and unfavorable valuations if/when the part of the notional is requested back.

A quick check on BBG using S&P 500 ETF (SPY) and 3-7y treasury ETF (IEI):

1y 4.21% OTM (on the spot price) call costs 3.72% of the spot

IEI yield is 1.36%
You can increase the carry by selling near ATM calls (less liquid and the longest maturity is about 6m) yielding extra about 2% p.a.

So, buy OTM call on the SPY with the cost of 3.72% p.a., buy treasury ETF and sell OTM call on it yielding about 3.4% p.a.

The rest should come from a management fee (1%?)

There is the duration risk, so you can use fixed maturity treasuries (or a strip of them like for hedging autocalls) instead but it still gives you exposure to the duration risk when the notional is requested prematurely.

For the Stoxx 50 index, you can also get a pickup in yield buy buying 1y SX5E dividend futures (about 3%p.a. currently).

Finally, for many small banks, getting funds for 10y would probably cost more than 4% p.a. (the cost of 1y OTM calls) and there was some recent regulatory relief for such tracker certificates (they can include the outstanding notional in some capital buffers) so that there are funding incentives for these banks to issue such products.

Hydraskull


Total Posts: 1
Joined: May 2017
 
Posted: 2017-05-15 14:27
Here's the major point that everyone's missing:

Insurer does not invest in the 10-year treasury yielding 1.76%.

Insurer invests in credit-risky fixed income, yielding more like 4% after defaults and expenses.

Now your option budget is a lot richer.
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