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4

No there is no way since the calculated internal rate of return $r$ is by definition defined as: $0 = \sum_{i=0}^{I} \frac{C_{i}}{(1+r)^{i}} $ You need to know the entire cash flow distribution and its timing if you want to compute the Pooled IRR. One advantage of IRR is that it takes the irregular timings of cash flows into account, logically its ...


4

Your second formula regarding the sum of day-to-day returns collapses as follows: $$ \begin{align} R_{weekly,2} &= \text{log}(Price_{Mon}) - \text{log}(Price_{Sun}) \\ &+ \text{log}(Price_{Tue}) - \text{log}(Price_{Mon}) \\ &+ \dotsc \\ &+ \text{log}(Price_{Fri}) - \text{log}(Price_{Thu}) \\ &= \text{log}(Price_{Fri}) - \text{log}(...


3

Exact solution: Assume we agree that for $y_1:=IRR(CF1)$, $y_2:=IRR(CF2)$, $y:=IRR(CF1+CF2)$, the following equations hold by definition: $$-1000+\frac{100}{1+y_1}+\frac{100}{(1+y_1)^2}+\frac{1100}{(1+y_1)^3}=0$$ $$-200+\frac{20}{1+y_2}+\frac{30}{(1+y_2)^2}+\frac{1}{(1+y_2)^3}=0$$ $$-1200+\frac{120}{1+y}+\frac{130}{(1+y)^2}+\frac{1001}{(1+y)^3}=0$$ These ...


3

The dummy function is always used to construct non-linear models. In your model, it is interpreted that the announcements have an non-linear effect on the return. So it is incorrect to say it is a linear regression problem, it should be called as a non-linear regression problem. In total, it means the announcements have asymmetric effects in explaining the ...


3

SMB is controlling for small stocks. Small and thinly traded are not equivalent. For instance, for most of its history, Berkshire Hathaway was a large stock, but thinly traded (b/c of its high price). There are a number of ways to handle liquidity risk. If you're looking to supplement a Fama-French regression, Pastor and Stambaugh (2003) uses order flow ...


3

Does this mean that correlation is 40%? No. Very simple example (in R). Let A and B be stocks with returns stockA and stockB. Consider following example: stockA = c(0.05, 0.04, 0.05, 0.06) stockB = c(0.01, 0.02, 0.03, 0.02) mean(stockA) mean(stockB) cor(stockA, stockB) stockA = c(0.04, 0.05, 0.05, 0.06) stockB = c(0.01, 0.02, 0.02, 0.03) mean(stockA) mean(...


2

The correct formula is to compute multi period gross returns as products of single period gross returns. Conceptually it is equivalent to calculating the return on a self-financing portfolio initially made of 1 unit of stock, with each cash dividend reinvested in more stocks at the ex-dividend price.


2

When position = 1, then you are long the S&P ETF. When position is -1, your portfolio consist of a short position of -1 S&P ETF. You will therefore have a vector like $Pos = (1,1,1,1,1,-1,-1,-1,-1,1,1,1,-1,-1,-1, \ldots)$, that will give you the evolution of your portfolio. Your returns are then the daily returns on the S&P multiplied by your ...


2

Yes, that can be really sophisticated even using such nice tools as pandas. But the basic idea is to find position enters & exits to derive cashflow. Here is my code to derive all that stuff from generated signals (in my backtester signals are fractions of 2 stocks in portfolio for each moment). I hope I've found all bugs here, but no warranties. ...


2

To answer you correctly we'd need to see the exact inputs of your regression... and I doubt you can mix easily linear and binary variables like that. If the market return is 1% at time $t$ do you have $R_{m,t} = 0.01$ or $R_{m,t} = 1$. Same question for $R_t$ Assuming both are using the "0.01" convention, then a move of $1\% = 0.01$ results in a move of $\...


2

Your opinion is correct. There is simply more information about risk-reward encoded in the Sharpe ratio than cumulative returns. The other thing that's important to know is that whatever ratio you choose is simply a social construct or conventional benchmark that people use to compare between each other. The ratio is only useful insofar as other people are ...


2

Another way to skin cat: # risk-free = 0 require(quantmod) require( PerformanceAnalytics) getSymbols('DJIA', src='yahoo', from = '2009-01-01', to ='2014-12-31') price <- Cl(DJIA) simple.ret <- price/lag(price)-1 table.AnnualizedReturns(simple.ret,Rf=0)[3,] # [1] 0.7267 log.ret <- na.omit(ROC(price)) SD <- sd(log.ret)*sqrt(252) R <-...


2

This is how people usually approach calculating SR with logreturns: library(quantmod) getSymbols('DJIA', src='yahoo', from = '2009-01-01') price <- Cl(DJIA) log_ret <- log(price/lag(price,1)) mean_log_ret <- mean(log_ret, na.rm=T) sd_log_ret <- sd(log_ret, na.rm=T) rf <- 0.0025 # benchmark SR <- (252 * mean_log_ret - log(1+rf))/(sd_log_ret*...


2

Apply your trading strategy to history. Convert account equity to USD by applying historical USD/JPY rates. Calculate VAR/returns as usual. Remember, VAR calculated in such a way will underestimate the impact of extreme events: i.e. 95% VAR will return you minimum of what you can lose on 5% trading days.


2

Is this for one firm only? Is there positive and negative announcements (ie do the abnormal returns differ in sign)? As per Binder (1998): $$R_{it}=\alpha _{i} + \beta _{i}R_{mt} + \gamma _{i}D_{i} + u_{it} $$ where the coefficient $\gamma _{i}$ is the abnormal return for security $i$ during period $t$. If the events tend to affect the security prices both ...


2

As far as your second model concerned: Abnormal returns for good news is $\beta_4$ The t-value of 3 tells it is significantly different from 0 The model does not account for effect of bad news so the effect of bad news will mostly be found in spikes in residuals around time of bad news releases. $\beta_0$ is return when all other factors in the model (...


2

The best way to answer the question is to look at the data. For example, on H&M in April 2000: Close Price Div 31/03 240 13/04 236 14/04 225 1.35 28/04 238 ThomsonReuters, Bloomberg and Factset do the following calculation for the return (+/- rounding): r = 236/240 * (225 + 1.35)/236 * 238/225 - 1 = -0.24% ...


2

Computing returns is one of the first things you learn when you start studying finance but I believe it's one the trickiest one once you get to complicated cases. The source you mentioned seems actually very good to me and it already takes into account different approaches and different subtleties like dividend payment. But this is in fact only the top of ...


2

First I thought about voting to close this question as it deals with Matlab synthax a lot. I ignore the Matlab stuff. You have 5-minutes data. So an estmator of volatility over any sample of size $N$ (e.g. 100) will be an estimator of the vol of your 5-min returns. Usually volatility is quotes as "per annum" or "pa". This means that using the square root of ...


2

Each of these can be used, but each has serious drawbacks. No. 1 is inaccurate unless you use $N>>10$ years of data. But decades of data may not be available or may no longer be relevant to today's economy. No. 2 is good except that the CAPM has been rejected by empirical tests. More advanced models from Asset Pricing Theory may be helpful (FF3, FF5, ...


2

If I understand your question correctly; the (expected) return always depends on the weights that the respective factor has in the portfolio, regardless of the risk. You are trying to find the optimal portfolio (given risk with highest return, or given return with lowest risk) so in the first step you try to diversify out the risk (and get the weigths for ...


1

Portfolio return is simply weighted return of parts (and NOT the formula mentioned in your post) - e.g. if you invested \$100 total equally among the four funds (\$25 each), and each of those funds earned 1% on average, then on aggregate you made 1% return on \$100 and not 4%. The trick (and the answer to your Q) lies in how you calculate these weights!! ...


1

I think you mixed up two aspects here: returns over time and returns over sectors (your columns). Your citation refers to a smoothing technique for portfolio returns over more than one time period where the portfolio consists of several sectors (might be even single stocks). That would be your rows (funds) but I cannot see the time periods here (which should ...


1

This is really the Campbell-Shiller (1988) decomposition: one of the key contributions leading to the 2013 Nobel Prize. The idea is very simple. By definition, the return between today and tomorrow is $$R_{t+1}=\frac{P_{t+1}+D_t}{P_t}$$ You can invert this: $$P_t = \frac{P_{t+1}+D_t}{R_{t+1}}$$ Take logs ($log P_t = p_t$ , $logR_{t+1}=r_{t+1}$ , $log D_t=d_t$...


1

I believe a few things need to be said here. First, returns are usually calculated (END_VALUE-BEGIN_VALUE)/BEGIN_VALE. There are other ways, but this is what is usually used, and much arguments can be had on what "value" actual is. Second, data frequency should be aligned so daily standard deviation should be aligned to daily expected returns. Third, the ...


1

IRR and MIRR are probably the two textbook answers to your question.


1

You could roughly estimate it by approximating the cash flows (which you do not know in full) using some "reasonable" simplified model. One example of such a model would be a cash flow of the form $$-\mathrm{investment}, 0, 0, \dots{\small (n-1 \text{ zeros})}\dots, 0, \mathrm{returns}$$ Such a simple cash flow has IRR $r$ iff $$ \mathrm{returns} = \...


1

Raroc is a risk based profitability measure. As you pointed out the connection to Basel is the use of the Capital. As far as I know, in many banks it is used for steering of the yearly capital allocation. However, I believe that in the near future(see Basel 4) it will become more important to directly steer with economic capital.


1

For the t ratio, you should re-parameterise your equation so that $(β_0+β_4)$ is treated as one coefficient, say $\gamma$ or a coeff of a single variable. you cannot use one's t ratio for making inference on the other. $β_0$ is the average return on this stock, the coef on dummy variable absorbs the abnormal returns. You could do this: $$R_t=\beta_0+\beta_{0}...


1

It is the same. With enough data, you could not reject the null γ1=β2. You could test that with simulation. See this with R: ## set.seed(12456) ns=500 t=1:ns D[]=0 D[t>.1*ns&t<.33*ns]=1 rm=rnorm(ns,.01,1.5) ri=0.01+1.2*rm+.15*D+rnorm(ns,0,.5) plot(ri~rm,col=D+2) #Model 1 summary(lm(ri~rm+D)) #Model 2 (m1=lm(ri~rm)) res=resid(m1) summary(lm(res~...



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