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Whether it's called volatility pumping, rebalancing premium, or Shannon's Demon it would just be a form of replicating a short gamma option strategy (eg. selling straddles). Intuitively, you are systematically selling at higher levels and buying at lower levels. The payoff for continuously rebalancing an equity/cash portfolio without friction when the ...


5

You may find the following paper worthwhile. It addresses most of the above points (and many more) in a systematic way: Dubikovsky, Vladislav and Susinno, Gabriele, Demystifying Rebalancing Premium and Extending Portfolio Theory in the Process (May 20, 2015). Available at SSRN: https://ssrn.com/abstract=2927791 or http://dx.doi.org/10.2139/ssrn.2927791 ...


4

There are some technical problems with using your previous weights as priors (that is, they are point measures), but yes, the Black-Litterman framework is suitable for this. You can essentially include any view point you have on the market within the model and let it affect your position size. This also includes views on transaction costs (based on such ...


3

It is hard to tell, because means and standard deviations are hard to estimate. Take a look at the example below from De Miguel et al: The row you are interested in is the third row ($mv$). They simulate normally distributed data, and realise that only when you have 6000 months of data (i.e. 500 years), mean variance starts to be close to the true sharpe ...


3

Portfolio as it stands: 300% A -100% B Total: +200%. Ratio 1.5:0.5 Short additional 50% B. Now: 300% A -150% B 50% Cash Total: +200%. Ratio 1.5:0.75 The problem is that you have to rebalance vs the total value of the portfolio. To get back to having the amount of A being 2x the portfolio total, you need to buy more A, to get it up to 400%. I ...


3

First of all, AM is always greater than or equal to GM $$ x_1 + x_2 + ... + x_n \geq \sqrt[n]{x_1x_2...x_n}~\forall x_i \geq 0 $$ You can prove it by induction from $\frac{x_1 + x_2}{2} \geq \sqrt{x_1x_2}$ or put $f(x) = \ln(x), p_i = \frac{1}{n}$ to Jensen's inequality to get it. The equality holds when $x_1 = x_2 = ... = x_n$. For author 1 and 2, We ...


3

If two or more (I(1)) time series are cointegrated, then this means that you can find a linear combination of them that is mean-reverting. Thus, if you create a portfolio with weights that are proportional to this linear combination, then the portfolio returns will also be mean-reverting. There is a large literature on cointegration and asset prices and ...


2

The calculation of rebalanced portfolio returns using PerformanceAnalytics functions makes use of what the package authors call "end-of-period" weights. As described in the documentation for Return.portfolio, the rebalancing uses the weights for the last trading day of the period to rebalance the portfolio after the markets close on that day. As an ...


2

You can't really combine the assets' log returns. You should calculate percentage returns for the three assets. Then at each time step, the portfolio's total return is: $r(i) = 0.5 \times \text{asset1_return}(i) + 0.25 \times \text{asset2_return}(i) + 0.25 \times \text{asset3_return}(i)$ Once you've calculated the time series of the portfolio's returns, ...


2

As @Lliane explains, you are actually describing a position in which the underlying is rebalanced everyday, hence the compounding effect of the leveraged ETF vanishes. Maybe a bit of modelling can be helpful to illustrate the relationship between leveraged ETFs and volatility. Let $S_t$ be the value of the underlying and $V_t$ the value of a leveraged ETF ...


2

I disagree that these products are convex*. At any point in time, the ETF exposure to the underlying is linear, it's just that it changes through time. A 2x ETF will just have 2x exposure to the underlying - where the exposure is based on the nav at the point of rebalancing. Say the nav is \$100 per share, then it will hold \$200 of exposure to the ...


2

Both products actually have positive convexity, they will buy more underlying (SP500) when the price goes up and sell it when it goes down. However, if you hedge every day, you will just cancel out that gamma convexity. You have to let the position run a few days if you want to trade the gamma, because it is generated by the daily hedging of the 3x etf, not ...


2

Major indicies, like Bloomberg Barclays, publish two versions of the index. One is rebalanced daily and the other monthly. Returns are always compared against the monthly rebalanced index. Bonds with less than a month to maturity are typically excluded due to index rules. However, calls and other redemptions still happen mid month. These bonds are replaced ...


1

Yes, considerable. My old firm did loads of it. However knowing that the research exists is not the same as getting hold of it or using it. In general we could say that it is going to be a good place to start by avoiding periods where there is limited liquidity. In many commodity futures contracts, these are usually seasonal. In general I can also tell you ...


1

Preliminary calculations Consider a $n \times 1$ vector of asset returns $r_{it}$ for each time $t$, where each of it is calculated as $$r_{it} = \frac{P_{it} - P_{it-1}}{P_{it-1}}$$ i.e. simple returns, where stock prices $P_{it}$ should be adjusted for stock splits, dividends, etc. For calculating value weighted returns $r_{t}^{val}$ for each time $t$, you ...


1

It actually works if you convert the (time series) weight matrix to the frequency you want to use for re-balancing using, e.g. apply.weekly(weight_matrix). The return matrix should still be daily data. I.e. the following code worked for me: weight_matrix.w=apply.weekly(weight_matrix, last) r.p.dynRP.w = Return.portfolio(ret, weights=weight_matrix.w)


1

It rebalances on endpoints(R), you passed it quarters, so every quarter as determined by endpoints(returns,'quarters') it will rebalance using the last 12 observations. In your case there you called optimize portfolio on a dataset of 37 observations nrow(edhec["2006-08-31::2009-08-31"]) [1] 37 This should explain the discrepancy between the two ...


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