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Andrew,
Proof read your work; please send your email address to: "GRC at xn--hofst-fsa.com", so that I can forward my comments.
Jean
The flaw at the heart of this paper is that for strategies 1 and 2 to co-exist, the assumption of independence of returns is violated. If we have constant one hour volatility, then the likehood of of strategy B returning the same as strategy A is almost vanishingly small - SQRT(6) * Sigma is 99.28%.
The problem with such ever higher trading frequency approaches is that they are dependent on market liquidity and that is by and large fixed in the outside sense and terribly dependent upon the credit creation process in an inside sense. We really should expect increased high frequency trading to increase intra-day volatility.
There is a copious literature on the time properties of volatility - and one recurrent finding in that is that volatility does not scale as the square root of time as we move from daily to weekly to monthly and so on.
I have not yet read the paper here. However, if I were asked to address this question, I would first distinguish between ultimate sources of liquidity. By this I mean that I will treat liquidity arising from non-market sources - coupons, dividends principal repayments etc - differently from liquidity in a market (i.e. sale as the source of liquidity)
Then I would observe that liquidity has a cost - if this did not all assets would be liquid. This is contrary to many studies which consider it to be illiquidity which is costly. It follows that the negotiability of market instruments is costly - the option to sell at any time. This means that all holders of these instruments bear some cost even though who never sell.
We can go further and define investment as dependence upon the collection of non-market liquidity and speculation as dependence upon the market. Now time can be frought into the mix. We receive more dividends (coupons, repayments etc) as time passes, and the market speculative element declines. In other words the separation of the short and the long-term is the separation of the degree of speculation (market dependence) and the degree of investment.
By the way this resolves the disjunction between Beebower Brinson who attribute 90% or more of performance to asset allocation and Dimson, Marsh & Staunton who show that 90% plus of long-term investment returns are due to dividend income.
Will read the paper when time permits and revert again later
I myself have never looked at risk from this perspective and having in mind that time is the fourth dimension in our space it is a good idea to have it somewhere in the methods of risk measurement. Moreover, with today's computing technologies and almost instant information exchange it seems crucial.
The results are worth attention but I would kindly propose some elaboration in this study. If a market is open for 7 hours and an investor participates in it for just an hour it's all right.
An hour consists of 60 minutes. During the 7 hours he could participate in the trades 1 time for full 60 minutes, or 6 times for 10 minutes, or may be 12 times for 5 minutes, or you name it - could be 60 times for a minute. This is the idea behind the high-frequency trading, which according to some experts has increased the risk enormously during the last years.
I would very much appreciate the comments of the authors on that. Thanks a lot in advance!
What's your budget for compensating the reviewer(s)?
Yes there is a strong dependency relationship between time and risk. i relies to show this relationship for a very reasoning used in mathematics is called "the absurd reasoning" that I just ensure complementarity of the proposal means that there is no relationship between risk and time. if there is no risk during the implementation of a project in macro in the market. Project will then deploy easily and more quickly and we will win the time and the current statue of the market( price, customer, offer etc.). In contrast , when we have risk in the market so we will wait until the risks are culled so dependence between the two terms is very clear.