invest – high risk, high expected return – HY, currencies

In theory, high risk means high (expected, not historical) return. More specifically, if an asset is perceived as more risky, then investors would demand evidence that it would yield higher return.

Simplest example is the risky bond. Assuming zero coupons, both the junk bond and the gov bond has the same maturity value of $100. Junk bond is shown (Evidence!) to be more likely to default, so the current price is lower, leading to higher expected return. That’s the basic idea of risk premium.

A 2nd example is FX carry trade, like long INR/JPY. INR is expected to depreciate so investors demand higher interest.

Long spot in Turkish TRY is another example. High risk high interest.

well-researched != simple#BS, VWAP..

Some people say vwap is easy/simple, when they really mean it’s well-researched. They mean other benchmarks are lesser-known and more sexy. Actually, implementing algos to beat the vwap benchmark is not easy at all.

Some people say standard option pricing model (BS) is trivial. They basically refer to those fancy models like stoch vol etc. I think this is jargon arms race — “who knows the most jargon”. I feel the intricacies of BS model is well-researched but not simple. Is theory of relativity simple?

Some people say vanilla derivatives are simple (cf exotics). well, lots of publications, but many unsolved problems and unanswered questions.

some people say STL is simple. They probably refer to the fancier containers. I feel STL has lot of details we don’t understand.

Some people say java generics (and c#) is simple. They mean compared to c++. But still there are many design tradeoff and implementation details we don’t understand.

MktVal – basic concept (confusion) cleared

PnL is a cleaner concept than MV. PnL can be -ve/+ve/$0. For MV,

1) In the simple case of bonds and stocks (think of owning a house), if you buy an asset, the MV is always, always positive
1b) a long option position has strictly positive MV
1c) a unit of any fund has strictly positive MV

In these cases, there’s an upfront full payment to the seller, upon execution.

2) MV (position without upfront payment) can have -ve/+ve/$0 MV. (In practice, such a deal is always initiated with MV=$0.)
* futures
* fwd contract on stocks
* FX fwd
* Swaps never require upfront payment

5) FX is tricky
5a) at a money changer, physically buying an asset ccy, using our domestic currency (SGD), is similar to 1). Full payment upfront, so the asset we bought has MV > 0 at all times.
5b) trading a cross (not involving our own ccy SGD) — no upfront. MV can be -ve.

9) Online trading is more tricky. Let’s ban leverage:) Buying an asset ccy using our own currency (ccy2) should be very similar to 5a), but actually the amount of ccy2 doesn’t leave my account. Instead there’s simply a CCY1/CCY2 position recorded in my account. Fundamentally unlike physical trading. In this context, MV of any position can be -ve.

arbitrage definition – any time before maturity

My understanding of the mathematical definition of arbitrage is vague. (I think in real financial world the precision may not be relevant.)

Here is one interesting point – if portfolio A and B have identical terminal value, then any time before maturity, they must always have equal market value, otherwise arbitrage exists. But what if (short) selling or is restricted or trading over a certain period is restricted?

In  real markets, many factors prevent arbitrage

* no bid or ask when you notice a mispricing
* insufficient quantity in the bid/ask. You may wipe it out then wait in vein.
* trading restrictions by authorities,
** short selling disallowed 
* most common factor – wide bid/ask spread, so you can’t really make any money. I think this is the case in most securities including most options.

3 types – pricing curves (family video…

— R@P (range of possibilities) graph, where x-axis = underlier or parameter –
eg: price/yield curve
eg: hockey stick
— family snapshot –
eg: yield curve
eg: vol surface
eg: delta vs underlier spot price
— family video i.e. evolution over time –

high return, high sharpe, high beta

Initially we want high return, or equivalently, high excess return.

naivety 1: we are ignoring the variance of the return.

-} so now we want high sharpe ratio

naivety 2: we didn’t know that all the expected return over the next year will be mostly driven by the market return.

-} so now we use beta to guide our selection.

* We might want a high beta, magnifying market return

** small stocks tend to exhibit high beta

* We might want a low beta, resistant to market up and down

* We might want 0 beta like a time deposit or something uncorrelated with the market

mean reversion – vol^pair^underlier price

I feel implied vol shows more mean reversion than other “assets” (pretending eq vol is an asset class). In fact Wall Street’s biggest eq-vol house has a specific definition for HISTORICAL vol mean-reversion — “daily HISTORICAL vol exceeding weekly HISTORICAL vol over the same sampling period“. In other words “vol of daily Returns exceeding vol of weekly Returns, over the same sampling period”. I think in the previous sentence “vol” means stdev.

This pattern is seen frequently. To trade this pattern, buy var swap, long daily vol and short weekly vol… (but is it h-vol or i-vol??) I am not sure if retail investors could do this though.

In contrast, Stocks, stock indices, commodities and FX can trend up (no long term mean reversion). Fundamental reason? Inflation? Economic growth?

The (simplistic) argument that “a price can’t keep falling” is unconvincing. Both IBM and IBM – 2 yr option can rise and fall.  However, IBM could show a strong trend over 12 months during which it mostly climbs, so a trader betting big on mean reversion may lose massively. The option can have a run, but probably not too long. I feel volatility can’t have long term trends.

A practitioner (Dan) said mean reversion is the basis of pair trading. I guess MR is fairly consistent in the price difference between relative value pairs.

Interest rate? I feel for years IR can trend up, or stay low. I guess the mean reversion strategies won’t apply?

I feel mean reversion works best under free market conditions. The more “manipulated”, the more concentration-of-influence, the less mean reversion at least over the short term. Over long term? No comments.