recombining tree requires Markov

Only a subset of HJM models have deterministic drift and vol. Without the deterministic nature, the Monte Carlo simulated binary tree would be non-recombining. See [[Hull]]

fwd contract arbitrage concept - less useful

label - fwd deal

The basic relationship (between spot price, fwd contract price, T-maturity bond price..) is intuitive, low-math, quite accessible to the layman, so I decided to really understand it, but failed repeatedly. Now I feel it's not worth any further effort. It's not quitting. It's saving effort.

- interviewers won't ask this
- real projects won't deal with it, because the (arbitrage-enforced) precision mathematics simply doesn't manifest in the real data, perhaps due to bid/ask spread
- Only financial math literature makes extensive use of it

I think this is like the trigonometry or the integration techniques -- you seldom need them outside academics.

equity swap, according to (my interpretation of) Pravin

Monitor the index (say spx) value now and 12M later. If that return is, say, 22%, then I pay you 22% of notional, on that future date.

Today, however, you pay me a fixed x% of the notional.

So the contract always references some index.

a few benchmarks in finance (vwap, sharpe...

Investment Performance benchmark - Sharpe
Investment performance benchmark - various indices
Investment performance benchmark - risk free rate
Investment performance benchmark - value benchmark and size benchmark. See the construction http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library/f-f_bench_factor.html

Execution benchmark - vwap. I feel this is the natural, logical benchmark. "Did I sell my 5000 shares at yesterday morning's average price?"
Execution benchmark (2nd most common) -- implementation shortfall (very similar to arrival price)

finance model -- various meanings, very briefly

I feel a financial model is any math that describes/explains/relates/predicts economic numbers.

A "model" means something different in buy-side than in derivative pricing including complex structured products.

On the buy-side, I feel a model is like a regression formula that Predicts a (single?) dependent variable using several explanatory variables. In simple words, such a model is an alpha model, which is related to a trading strategy.

S&P 500 index - various symbols

Background -- There are various symbols, some of them (like "SPX") have multiple unrelated meanings. No one-to-one mapping. Not even many-to-one mapping like aliases.

The S&P 500 is often quoted using the symbol "SPX" or "INX", and may be prefixed with a caret (^) or with a dollar sign ($).

"GSPC" is another symbol

merger arbitrage, basics

Naive strategy -- between announcement and completion, buy the target company, sell the acquirer.

If aborted, we are likely to lose, as prices return to normal.

To hedge this risk, we can sell an index. A market decline is often correlated with a failed merger.

extreme long-short allocations by MV optimizer

This is stressed over and again in my MV optimization course...

 

Suppose we have only 2 securities with high correlation.

 

Often one of them (AA) has a slightly higher Sharpe ratio than the other. The optimizer would go long a few hundred percent (say 300%) on it, and short 200% on the other (BB). These allocation weights add up to 100%.

 

If we tweak the historical mean return a bit so AA's Sharpe ratio becomes slightly below BB, then the optimizer would recommend go deep short AA and deep long BB.

 

This is a common illustration of the over-sensitivity and instability of MV allocation algorithm. In each case, the optimization goal is maximum Sharpe ratio of the portfolio. Why Sharpe? MV

 

risk premium - dynamic factor models

 See post on static factor models.

A lot of econ theories and asset allocation models produce dynamic estimates of next-period returns. One example is the dividend-yield model, based on dividend-price ratio. If my DP data indicates some stock is going up next year, how would the econs  theory suggest me do?

Mark Hendricks’ HW1 has a (theoretical) example. Not sure how practical it is.

risk premium - static factor models

#1 Assumption – time-invariant equilibrium, iid (or at least slow-changing).

All of the alpha, beta, lambda, steady-state mean/vol of annual returns on every security, correlations, covariance are iid ... All the year-to-year changes are attributed to the noisegen, but the noisegen itself is absolutely stable. Just like in natural science.

Even a fund is modeled as a fixed collection of securities, more fixed than any index.

I feel once we wrap our mind around this Fundamental Assumption, everything falls into place. Now the remaining task is to calibrate the alphas, betas, etc, using historical data.

The "value" index is a long-short portfolio of many, many stocks. Think of it as a security, with a higher "intrinsic" level of return and higher "intrinsic" vol than the market. This is a typical high-risk-high-return security. Investors are rewarded for taking on the extra risk. 

Just how much extra return is in this reward? I used to think the reward must be high enough otherwise no investor would want to take on the risk. That would be a supply-demand theory, but I now I feel our Fundamental Assumption implies that the intrinsic volatility/excess return are a reward/cost that's "precisely" measured and published, so each investor can choose to take it or leave it.

The intrinsic excess return in the steady state represents the excess risk inherent in this "value" portfolio. This portfolio has an "intrinsic" risk premium, i.e. an "intrinsic" excess return. Suppose it's 12%. If an investor JJ's portfolio has value-beta 0.5, that means JJ can expect, over the long run, 6% excess return due to this exposure. JJ could also have a size-beta, which would contribute another 4% extra returns.

Hi Victor,

Let me address these in order...

1.)  Yes, lambda is the factor risk premium estimated from historic data.  A risk premium of .11 says that you get an EXTRA return of 11% for every unit of the factor beta which you hold.  You're right that this estimate is from historic data so we can't be sure about what the factor premium will be over the next 80 years.  That is why any asset manager would not just use historic data but also their own beliefs and forecasts about the future.

2.)  You're right that CAPM is the simplest example of a factor model, so it can be very helpful in understanding all the others.

Risk premium = expected excess return.

Risk premium of a factor (lambda) expected excess return on holding that factor

Beta is a measure of risk.  It tells you how much covariance risk the security has.  There are many betas we could measure, each would tell us about a different type of covariance.

Value beta is a covariance with a portfolio of value stocks, which means stocks with large book valuations compared to stock-market valuations.  (Or large Earnings compared to Stock Prices.)

Size beta is a covariance with a portfolio of small stocks.  

"Size" risk prmium is the expected excess return from holding small stocks.  

The FF factor model says that for each unit of "size" beta a stock has, it will get an extra amount of risk premium, equal to the risk premium of the portfolio of small stocks.

I hope this helps.  For more on the CAPM, see the references in Lectures 3-4 of FINM 367, or really look into any decent book on asset pricing.

professional option traders

Professionals sell calls and puts. (Retail investors buys them.). These are "High probability" trades, i.e. high chance of profit. Given this zero-sum game, it follows that the option-buyers do low-probability trades. This isn't a risk-neutral world. Retail is risk-averse.

There are real risks that the option could get exercised, so the option sellers always need some protection.

Professionals “always” trade pairs

Professionals "always" trade pairs like

 

-          Relative value pairs

-          Option "strategies"

 

My problem with pair trading is the commission or bid/ask spread.

 

 

 

__Tan Bin (+65)6530 1386 OC Centre #17__

 

securities with negative value

Some securities can have positive/negative values for the holder. I don't know many asset classes in this category. (If indeed there are only a few, then they must be important). What I know -- Fwd/futures contracts. These contracts are fundamental to almost all derivatives.

Most traditional securities (assets?) have a purely positive value – stocks including ETF, (junk) bonds, options, commodities, real estate, MBS...

How about swaps? I think like the fwd contract, the execution price is chosen to give both holders $0 value on trade date. After trade date, either holder can have a "position" with a positive  or negative value.

How about structured products? I guess often falling into this category. Usually between 2 holders – a dealer and an institution.

tick data volume

there are many ticks (trades) during each minute of the day. Active securities during busy hours can have 20-30 ticks in one minute
alone. With 390 minutes in a typical stock exchange trading day, many stocks end up with well over 5000 ticks per day.

CDS pricing, briefly

use bid/ask from market to derive the cash flow including premium and the "disaster" compensation amount. This gives an implied default density or hazard rate. Plot the hazard rate along maturity. You get a credit spread curve.

Then you can price all related credit instruments using this credit spread curve.

order internalization

I guess internalization is not automatic. Special logic needed.

---------- a veteran's answer ----------
"I don't think we have logic locally to cross against firm automatically. The trader would have to send an explicit order to cross against firm. There is a Smart Order Router layer that intercepts order and they may have some logic there to automatically cross against firm."


On 6/20/2012 3:10 AM, Bin TAN (Victor) wrote:

See job spec below about "internalization". Is there non-trivial business logic about that in your system? I guess if a client places a limit buy order and the internal best offer is better than the exchange best offer then do it internally.  Is it that simple or there are hidden complications.

Not sure about market orders but I guess if the internal best offer is better than the exchange best offer then obvious...

profit margin in equities

* there is Direct Market Access (DMA) - like brokers / trading houses that facilitate equity trades - extremely low margins
* there are block trading venues that facilitate low-impact block trades between buy side vendors - high margins
* then there are various equity derivatives, like options trading and equity swaps - that's another ball game

risk management in wealth management

* product concentration risk. As a unit we want to stay x% in eq, y% in cash equivalent, z% in special investment... When we deviate, we need to know.

* client risk -- sub ledger to feed to secDB so we could analyze risk for each client.

rule based margin calc + stress test (GS prime brokerage?)

Start with basic margin calc used in my 1997 investment, or as described in http://thismatter.com/money/stocks/margin.htm.

Then apply rules. Rule-based calculator recognizes known hedge strategies and picks out each pair (or 3-some ...) of positions in a hedge. These tend to reduce the margin requirement. Known as margin release??

Lastly, apply stress test to simulate worst cases. One of the worst cases is the worst worst. In the worst worst, price can be 5%  worse then normal, so investor's margin requirement should increase 5% to cover that.

financial jargon: institutional clients

external hedge funds, mutual funds, pension funds, fundations... managed by *other* companies