# Questions tagged [returns]

The asset rate of returns is the profit on a particular investment; it includes any change in the asset value, interest, commission or dividends and so, all other cash-flows which an investors receive or pays due to the investment.

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### Results of Fama MacBeth regression

I have run Fama MacBeth cross section regression of of Excess Return of stocks on Idiosyncratic volatility, the log of market capitalization, book to equity ratio and Beta. I'm getting all significant ...
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### How do I maximize my expected utility of wealth?

Suppose I have a utility function say $U(p)=p^{1/2}$ and I bet on a basketball game. I have my initial investment, payouts and probabilities of winning, how can I determine the maximum I need to bet ...
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### How can a stock have negative returns but positive 3-factor alpha?

I've come across a research paper where for a specific period of time, the portfolio has negative returns (or roughly flat returns). During this same period of time, the portfolio's Fama-French 3-...
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### Overnight and intraday returns of stock index and ETF seem inconsistent

Figure 2 of the 2019 paper "Celebrating Three Decades of Worldwide Stock Market Manipulation" shows that 29 Jan 1993 to 31 Oct 2019, overnight returns (from close to open) of SPY were 1232% while ...
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### Time and asset weighted rate of return of a portfolio

If I have a portfolio with 3 initial assets on day 1 (say, stock 1 with beginning market value of \$100, stock 2 \$150 and stock 3 \$175) and after 10 days the stock 2 is sold for \$200, how can I ...
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### Bloomberg Treasuries PX_Last and daily returns

I tried to search for this specific question, although I didn’t found a conclusive answer. I have a dataset containing the yields of several T-Bills and T-Notes that were downloaded from a Bloomberg ...
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### Relationship between ROE and IRR

In the textbook I read the following: We can increase the present value of a share of common stock with a new investment only if $ROE > r$ , where $r$ is a discount rate (capitalization rate). ...
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### Autocorrelation in daily bond returns

I've been examining the returns of a few government bond series around the world. I found out that some have a positive daily autocorrelation. It's not big, but still seems at odds with efficiency. ...
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### What's the interpretation behind this GARCH modeling?

I have an ARIMA model for monthly returns of the brazilian stock market index. Then I test the residuals of the model for ARCH effects. The ACF/PACF of squared residuals show that there are no ...
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### Source for derivation of acquisition price for given IRR and cash flows

Does anyone know a quotable source - book/academic or practitioner's paper - that derives the acquisiton price for a target firm when the buyer's desired IRR and all cash flows over time of the target ...
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### Predicting stock returns using principal components of macroeconomic variables

I'm trying to detect return predictability by regressing stock returns on the first couple of principal components of a set of macroeconomic variables. I'm doing this for different stock styles such ...
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### General to specific approach to modelling

I am trying to find the relationship of stock indices across the world. This has been done by the literature, however, I am wondering about the methods chosen. I have decided to go with what I think ...
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### Sample distribution of cross-sectional statistics of returns

Currently doing an application of VaR on sample of industry portfolios in the US. I have a matrix of $n$ industry portfolios with $m$ time-series observations. I calculate cross-sectionally (for each ...
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### How to apply derived beta to daily change?

I've taken three months of price return data for two instruments and calculated a $\beta$ between the two using the formula $\beta = \frac{Cov(x,y}{Var(y)}$ with the goal of estimating what the ...
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### Black Litterman - numerical instability

I am trying to work out the formula for the posterior mean in Black Litterman's model assuming 100% confidence : Ref: https://corporate.morningstar.com/ib/documents/MethodologyDocuments/IBBAssociates/...
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### Computing squared returns given differential equation for prices

I am looking for general advice on how to start tackling the problem below. My background in math is fairly bad when it comes to stochastic differential equations, but if you have any recommendations ...
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### Bootstrapping to Judge the Fit of a Sampled Return Distribution

Consider the following: I have sampled yearly stock returns from a specified distribution. What I want to do is compare how well my sampled distribution fits the empirical distribution of yearly ...
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### Generate P Value from stationary bootstrap following Politis & Romano (1994)

For my master thesis I am analyzing the performance of trading strategies. For this I need to avoid data snooping by utilising the FDR approach. I follow closely the procedure presented by Bajgrowicz &...
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### Is variation in price-dividend ratios that is attributable to excess returns due to variation in returns or variation in risk free rates?

Cochrane and Fama show that "all variation in price-dividend ratios corresponds to changes in expected excess returns -risk premiums- and none corresponds to news about future dividend growth". Is ...
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### Confused on interpretation of betas/alphas in regression in finance

I ran a regression on two stocks. I don't have the data in front of me, but it is a more conceptual question. Let's say SP500 returned a total 23% return over this time period and MSFT returned 9%...
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### Calculating Asset Returns

The question pertains to a simple phenomenon. There is gold futures listed on Exchange A and Exchange B. Exchange A and Exchange B overlap times with A and B starting 8 hours later and A and B ...
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### Sampling and/or asymptotic distribution of a function

Assume we have the following function: $$f(p) = \frac{1}{(1-p)d}\ln\left(\frac{1}{T}\sum_{t=1}^{T}\left[\frac{1+X_t}{1+Y_t} \right]^{1-p} \right)$$ where $d$ is a constant $T$ is a constant $X_t$ ...
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### Long/Short portfolio return

Suppose I have a Po with one long, one short positions and some cash (to balance the short + 50% margin) as shown below: ...
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### How to Compute Returns from Cumulative PnL and Price Data for Portfolio Optimization in Algorithmic Trading?

I have a set of algorithmic strategies. Each strategy focus on a specific financial product and generates entry and exit Long or Short signals. So for each strategy we can have periods in which we are ...
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### Calculating returns on sequence of trades with zero starting capital

Background I am trying to calculate the returns on a sequence of trades performed by an entity, where I do not know the starting capital. Therefore I assume a starting capital of zero. From these ...
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### Visualizing Drawdown

I want to replicate the image below: Does anyone have an idea how to do this in Python. To be specific; I am only having problems plotting the blue shade and the blue lines.
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### Optimized Method to Calc Real Rates of Return From Monthly Nominal Rates

I wrote the following VBA code to calculate real rates of return using Robert Shiller's dataset: Note: This calculation is for forecasted returns so I have no prices available to do the calculation by ...
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### Constant maturity bond fund returns in downward sloping curve

Assume the following: we are running a constant maturity bond fund (10yrs) all zero coupon bonds to maintain the maturity, we buy bonds of 10y and sell the 9y bonds 1y later price of 10y bond is 100, ...
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### How to calculate historical returns and variance for a non-BAH trading strategy?

Suppose i have a strategy that is not buy-and-hold type of strategy. It can have unique entry timing and unique exit timing for a single asset and both long and short positions will be allowed, and ...
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### How to properly calculate leveraged returns

Imagine we have a certain price movement, where the price starts at 1000 and ends at 1200, with some fluctuations in the middle. For the sake of the example, imagine it's hourly timestamps, and it's a ...
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### Determing "fair" implied volatilities for SPX options

I'm trying to come up with a method to calculate fair IVs for SPX options based on historical data. I can't find much information on this so here's how I've thought to do it: Determine a metric for ...
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### What is the proper way to calculate cumulative return when only a portion of the portfolio is invested?

I have a hypothetical investment strategy that returns $x$ amount after $n$ days for a $1/n$ portion of the portfolio. I want total cumulative portfolio return. Is this right? Basically, I calculate ...
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### Filtering a time series of returns by deleting some points

I have a time series of returns of an asset (call this $X_t$) which I have verified to be stationary. Let's say I generate a new time series $Y_i$ which is a filtered version of $X_t$ (that is I ...
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### Estimating Appropriate Risk Premiums without Comparable Project Data

Objective I wish to estimate an approximate reasonable return (a) for a project, given its inherent risk and risk-free rate, and compare that to the anticipated project return (b). Such that, all else ...
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### Bias-Variance tradeoff for Covariance Estimation w/ Different Frequencies

In general, what does the bias-variance tradeoff look like when estimating covariance matrices with varying return frequencies (i.e. daily, weekly, monthly returns)? From my observations I've noticed ...
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### Equity and Credit Portfolio Return

This might sound like a trivial question but would appreciate the answer. How would you calculate the return of the portfolio consisting of only equity and credit instruments? For example, consider ...
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### combining forecasts at different time horizons

I define a prediction of return of an asset as the following: at time $t=0$, I use my data and output that I expect the asset to make the following returns (in expected value) in the next n intervals \$...
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### How to calculate the portfolio risk and return if daily share prices, volume held on that day is given for all assets?

The problem is with the changing volume of assets which changes the weights. I want to use the formula for portfolio risk but cannot figure out the weights. Should taking average weight of an asset ...