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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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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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55 views

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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21 views

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 ...
3 votes
1 answer
1k views

How do you define returns when price may be negative (electricity price)?

I'm trying to model GARCH volatility on electricity prices. Typically the first step is to use prices to obtain log returns to make them stationary. I have encountered a small problem however: ...
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1 answer
120 views

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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13 views

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, ...
1 vote
1 answer
263 views

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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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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206 views

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 ...
0 votes
2 answers
285 views

Estimating distribution of rate of return

Let $f[t]$ be the price of a stock at time $t$. We can calculate the rolling rate of return of the stock in a window of length $n$ by computing: $$r[t] = \frac{f[t] - f[t-n]}{f[t-n]}$$ $r[t]$ is ...
30 votes
11 answers
25k views

Should I use an arithmetic or a geometric calculation for the Sharpe Ratio?

What are the advantages/disadvantages of using the arithmetic Sharpe Ratio vs the geometric Sharpe Ratio? Is one more correct? Or is one better in certain circumstances?
2 votes
0 answers
146 views

Bound on path length of a stock price

Consider a time series $(S_i)$ representing a stock price (say close prices of one minute candles). Let $\Delta$ be a quantization step (could be the price step in the strike prices of the ...
-2 votes
1 answer
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How to calculate the BHAR (Buy-and-Hold Abnormal Returns)?

I am doing my research related to IPOs long term performance. For the $\text{BHAR}$ (Buy-and-Hold Abnormal Returns) formula, I just want to clarify the formula is that always compare with the first ...
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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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87 views

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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1 answer
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How to compute % return of a strategy with Vega notional [duplicate]

I'm currently running some backtest on a strategy 2 legs and where the product traded is straddle. I aim on this strategy to be Vega neutral thanks to a balance between 2 legs. Thus, I deal with Vega ...
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2 answers
144 views

Simple concepts around return, VaR, etc

In a simple setup, let's say $(w_1,w_2)$ are weights invested in assets $1$ and $2$ with prices $S_1$, $S_2$. I only saw discussions when $w_1 + w_2 = 1$, even if short selling is allowed. Suppose $...
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2 answers
127 views

How to get returns when investment capital is changing?

This question came out of the Kelly rule. Curious how returns are calculated when allocated investment is changing on the course. Let's say an investment start with \$100, if the investment hasn't ...
2 votes
2 answers
3k views

cumulative return calculation, disagreement

A friend of mine and myself are having an argument on how to correctly determine cumulative return. The dataset has monthly return data and we are trying to determine the 6-month cumulative return. ...
1 vote
2 answers
271 views

Return forecasting for portfolio optimization

I have some questions related to forecasting returns and how it's used to generate the inputs for portfolio optimization. First, I want to understand why factor models such as FF- 3-factor model are ...
1 vote
4 answers
453 views

How to calculate return on investment for an adjustment to a complex options position?

Say I currently hold a set of options positions with the same symbol/expiry that collectively have a net present value based on the estimated value at expiration of +10. I could also liquidate the ...
1 vote
1 answer
50 views

Scaling variables (Fraction vs % vs log) when regressing twelve month returns

Dear Stack community, My question is the following; If my dependent variable is twelve month returns. And as independent variables I have fiscal year variables like ROA and log variables like the log ...
2 votes
1 answer
202 views

Calculating Portfolios Covariance via Bilinearity with Log or Simple Returns

I'm wanting to calculate the covariance between two portfolios $A$ and $B$ which are allocated to assets $X_i$ (where $i \in \left[1, 2, \cdots, N \right]$) with weights $\vec{w_A}$ and $\vec{w_B}$, ...
1 vote
1 answer
318 views

Compounding vs Annualizing Returns in a Portfolio Optimization Context

This might be a rather basic question that might be closed... but I can't for the life of me understand why in many Google search results the annualization of daily returns is done like this: r_yearly ...
-1 votes
1 answer
57 views

How to calculate weighted return of two stock prices? [closed]

I have 2 list of returns A = [0.00538467, 0.04701923, 0.00170811,...] B = [0.00299271, -0.0060228 , -0.07761099,...] I take long position in A and short in B. How to calculate the total return and ...
1 vote
1 answer
119 views

Contribution to compound returns

When trying to recreate this chart from Deutsche on contribution to compound returns of an asset class I'm using log returns of each percentile group (bottom, mid, top), take the sum and divide each ...
1 vote
1 answer
112 views

Tricky question about returns [duplicate]

I have a list of monthly returns. -10% -20% -70% -30% -15% -60% The total end return is -94.859%. Because you calculate = 100 x (1+ -10%) x (1+ -20%) x ... Now I ...
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1 answer
83 views

covariance between squared returns and past returns

Let $y_t = \sqrt{h_t} \epsilon_t$ where $\epsilon_t\overset{ iid}{\sim} N(0,1)$ $h_t = \alpha_0 +\alpha_1 y_{t-1}^2+\beta_1 h_{t-1}$ with $\alpha_0>0, \alpha_1>0, \beta_1<1,\alpha_1+\beta_1&...
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0 answers
85 views

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 ...
0 votes
1 answer
49 views

Need Guidance on Analyzing Financial Data Across Multiple CSV Files in R [closed]

I'm new to R but experienced in Stata. I'm working on a research project involving 39 countries, each with 100+ years of daily financial data (date, high, open, close, return), along with USD exchange ...
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24 views

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 ...
2 votes
1 answer
332 views

How to Normalize Weights When Weights don't sum to 100%

I'm working on a take-home assignment for a company. They want me to calculate the return of a portfolio of securities over time, given the returns of the securities over time and the initial ...
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2 answers
162 views

how to calculate YTD return including the paid dividends

I am looking for a way to compute YTD return and I found this question (calculate YTD return / find first available datapoint of a year in python), however, it seems that it does not include the paid ...
1 vote
1 answer
99 views

Fama French Factor adjusted returns

I want to understand the extent to which portfolio performance can be explained by the three Fama French Factor model. I use the following approach: Regress the portfolio's excess returns against the ...
2 votes
1 answer
220 views

Trying to understand the notion of required return

I have been thinking about the notion of required return lately. I am not familiar with a formal definition, but I have tried to reason my way towards one. Please let me know if my approach makes ...
0 votes
1 answer
122 views

Correlation between CDS return relevance

I see that there is much literature that uses the correlation notion in the equity returns to construct a graph or look into how they are related to one another. If we want to extend this to Credit ...
1 vote
0 answers
88 views

Daily returns over many days of two-stock portfolio - averaging

I'm reading Ernest Chan's book “Quantitative Trading: How to Build Your Own Algorithmic Trading Business 2E”. In example 3.4 of chapter 3, he defines: The daily return of a stock on day $d$ as $...
1 vote
0 answers
200 views

Total Return on Bond [closed]

I'm trying to calculate the total return (in %) on a 9% coupon 20-year bond with the following assumptions: reinvestment rate of 6% annually (3% every six months) terminal yield of 12% (semiannual ...
1 vote
2 answers
8k views

How does one calculate carry-roll-down theoretically assuming expectations of short-term rates are realised

I am not asking for an explanation that is hugely quantitative, but rather one that is more intuitive. I am aware that there are different assumptions that one could take when it comes to carry-roll-...
1 vote
1 answer
341 views

Variance of the price from returns variance

Let's say that we have the variance of the daily return at $t_0$: $$\sigma_{r_{t_0}}^2=\text{Var}[r_{t_0}]=\text{Var}[\frac{S_{t_0}-S_{t_0-1}}{S_{t_0-1}}]$$ for price process $S_t$. Is there a way to ...
1 vote
1 answer
258 views

Figuring out how TradingView calculates the Sharpe ratio [closed]

This is the simplest backtest I've come up with, yet I can't figure out how TradingView has calculated the Sharpe ratio to be 0.577. I've set the risk_free_rate=0. Is it possible to extract the ...
6 votes
1 answer
278 views

Why can I use equilibrium asset pricing models to predict future returns?

This is a general question that applies to the CAPM and any version of the APT (e.g. the Fama & French three factor model). Speaking in terms of the APT: Assuming a simple one-index version of the ...
2 votes
0 answers
114 views

Does the expected return increase with variance for stocks? [duplicate]

I took a historical dataset of ~2600 stocks and computed the 30-day returns for non-overlapping windows, for a 9 year period. For the returns, I computed the mean and variance. Then I plotted the mean ...
2 votes
3 answers
12k views

Calculating log-returns across multiple securities and time

I've been getting very confused on the topic of calculating returns. To get cumulative returns in time, log-returns are used, but apparently log-returns aren't used across different securities at a ...
1 vote
2 answers
5k views

How to calculate "portfolio cumulative return" from individual price data and weight of them?

I'm trying to run backtest in a vectorized way using Python Pandas and need to calculate a portfolio cumulative return from price data and weight of asset data. I ...
2 votes
2 answers
829 views

How to annualize Sharpe Ratio if monthly returns are serially correlated? Calculation of autocorrelations

I am looking at a data set of 60 monthly returns (last 5 years) and want to calculate an annualized Sharpe Ratio. The usual way of doing this is to calculate the monthly Sharpe Ratio first, and then ...
0 votes
1 answer
868 views

long short portfolio sharpe ratio

What is the proper way to caluclate sharpe ratio for the long short portfolio? When I calculate daily return with no cost, I use this formula: (return for long k.mean()+ (-1)*(return for short k.mean()...
0 votes
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75 views

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 ...
3 votes
3 answers
472 views

How to identify daily returns as an unusual daily return given a dataset

I am currently calculating daily returns of a stock with the following formula: $$R_t = \frac{P_t - P_{t-1}}{P_{t-1}}$$ However, once I have the data, I am unable to establish a range to classify the ...

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