here's historical var of a portfolio of stocks looking back over last 250days Code: import Quandl portfolio=[100,200,500] wdf=Quandl.get([u'GOOG/NASDAQ_GOOG.4',u'GOOG/NASDAQ_AMZN.4',u'GOOG/NASDAQ_MSFT.4']) pval =wdf[-250:].diff().dropna() * portfolio pval.T.sum().describe() count 249.000000 mean 274.546185 std 1938.771031 min -4821.000000 25% -909.000000 50% 127.000000 75% 1522.000000 max 15914.000000
From the PDF: Page 3 Historical value-at-risk [/b]This metric can be useful in explaining risk to people who are less familiar with investment theory. Page 10 (Among some other objectives and other risk measurement indices) Objective: Maximize risk-adjusted performance. Possible key risk measure:Look for an investment or combination of investments with the highest Sharpe ratio. I think I like the Sharpe ratio so far. Or the information ratio? That gets more complicated. = OK. Question: Let's say we have Investment A with a 10% year-on-year return. Then we simply leverage investment a 2:1 to get Investment B which brings us 20% a year return. The question is, how the Sharpe or other important indices change following this only one change in the investment?
Kutk2, do not bring up the nonsense about Kelly Criterion having a related impact on future growth. We do know that from second to second might seem like a good timeline to place trades, but at the minus second where the trades happen at the exchange they are not convexed inversely without giving substantial indications of upside to wherever they move. Because it assumes 50/50 there is no person that should be using those and as the time interval increases so also must the win ratio increase because if it were to decrease the amount of the move is not comparable and this is determined to be a case of non-linearity because the trades happening cannot be done past 0 second and so any trade that can be outputted has to be done so with relative risk of the sharpe ratio of at least 1 because you should never take more risk than you have to to get the same return. If you are smarter about this latency causing the perils in the auction market structure we are either living through an age where 0 second is purposefully driven by the principal/agent dilemma to resolve transactions deemed to be profitable even if for microcents on the penny. I've been looking at the loadout reads on all the trades taking place between the bid and ask and they are getting astonishingly stupid in the number of decimals needed to claim NBBO bid at minussecond meaning any second or fractional microseconds cannot define where sound basic logic that what goes up must go down cannot be made in the history of the stock market because if it increases time by one unit of microsecond so also must there be a readout from the lines of ascii marking all of the decisions these computers make that for there to be zero second a lot of instrumental limitations prevent any sound definition from latency of there ever being a minussecond in which the time it took you is not just bearing on latency that if the entire market can only do 100,000 trades in a second then we are all in big trouble because that means 1 million trades trying to all do trades at the same time prevents there from being the microcosm where price had changed and began at close to 3 microseconds ago, say, and 3 microseconds ago being called 3 minus seconds is simply that unit of time that cannot be defined as categorically being anything but the manipulation of the exchange and its member broker dealers. If you have to measure a quantity of time, it will always be a quantity of time, but if you have a unit of measurement where somehow the minussecond made a computer realize that in order to give up this rash and baseless decisions to try to make minimum tick increments at one time is absolutely possible but only for the most well capitalized. It does not matter in what time frame it's in if there's profit then someone lost but there must have been gain for somebody. If microcosm sounds like the Hersheyesque writing style I try to bring to the table I'm terrified sometimes at the movements I see and just relax and play blackjack with myself for a little bit waiting for that reconfirmation that my interval will be right. My intervals are on daily and 16,807 contract bar charts and 5 minute charts. Those are the charts I've made the most money by using, especially daily predicting week to weeks long swing trades where I make over 5 figures so to paralyze the conversation with 50/50 Kelly Criterion does not allow anything but a game of quantity of money, not time, to move it in your direction. Some bastard trader got really angry with the market May 6th, 2010, a day after I got divorced and that could have been the most ruinous day of my life because I say that I survived and those after me will seek to live through it just to say they have so even if total loss is always abandoned down to the minussecond, at least there will be some fraction unit of time we can call to decimalized minussecond and if you discover the fractional basis of trading is just that, the people scalping for those miniscule amounts are really only doing so to change their price at least enough percent of the time to get out of the trades where 1:2 makes 2:1 bear on the upside is still possible today and used by practically every high frequency trader. In mine there is a difference because the unit of time is the quantity, and if anybody was making that bank buying 7 points from the low and selling 20 points from the high for over 275 points wouldn't you want to just let the 50/50 small tick interval big trader moves the pit and comes down on too many revealing that as gravity goes up so it must come down wealth is not that way because there is no gravity but the relativity of it to it's previous high, so you can just bet that will never see 666 on ES ever again because money has been created in too great a quantity for it to ever be losing again since at that level we create the fire that fumes the growth of prices of thousands of trades happening every second and admittedly some are larger than others but the others who stick around and poke there head out above the sand to where there's actually a whole body might be the very basis of creation so that one day there could be 2 or 3 or 4 bodies in the sand marking there presence by their bacterial interaction with the outside quantity of consumption available to the spawn. Even if we don't agree how to calculate risk, listening to a bunch of uneducated numskulls who haven't the foggiest idea why a risk standardized equation isn't the unit for all. Sortino works out to too many probabilities of the predictions you might expect being disappointing than you'd ever get with sharpe and why is a mathematical reason that if there are two divisions, one of a difference, and one of that difference to the standard deviation the numerator will always be positive, and this is why stock markets don't fall, they rise and flow but with that knowledge comes insider trading venues that have information deemed to be reliable that by placing trades at the minussecond where every trade that isn't yours must not have been NBBO NBBO is too much to explain about why if you always have a bid ask spread price can never go to zero for any company with money in it and whether that person who manages the company meant for the value to decline that far, it only approaches zero. It can never actually be zero due to logarithmic properties in financial markets and while derivatives can be exploited the same way there value is a true presence of time that cannot be dismissed as a figment of that last high frequency traders operations from placing bids and offers sizable to the exact NBBO at all times and the Exchange would disguise that process with minusmilliseconding split rate where the exchange is at all times finding clients to trade with, but always between them, and if you can do that Sharpe wins out the day because it means that as long as the security exists it's standard deviation can never be zero no matter how short the time frame unless so well capitalized.
The return isn't the only thing that changes... The volatility of your leveraged asset also does. I would highly recommend the papers by GMO's James Montier, such as the "Seven Immutable Laws of Investing" and others. They're really very good and you can find them out there easily.
Risk measure depends on asset and timeframe. It is more of an abstract concept like "love", for example. It all depends. For long-term stock investors the annualized standard deviation of the portfolio is a good measure of risk. For bonds things are a bit more complicated and you have to use duration and convexity. For short-term traders their risk is how much they are willing to lose via a stop-loss. Since this risk is almost controlable except during a flash crash or some black swan, most people prefer shorter timeframes.
I am reading this.: http://www.pragcap.com/wp-content/uploads/2013/07/Montier-James-7-Immutable-Laws-of-Investing-1.pdf
I heard this guy - https://en.wikipedia.org/wiki/Gary_Becker - referred love as intuitive cost optimization