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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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1answer
27 views

Value premium analysis - Equal or Value-weighted Portfolios?

I got a question regarding the analysis of the value premium in the U.S. stock market. The task is to use the market-to-book-value ratio to split the S&P500 in five portfolios (rank 1-100,101-200,...
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18 views

Error distribution algorithms in performance attribution

Are there any known & generally accepted methods of scaling each return in a period such that the total cumulative return equals a more desired amount? For example, 0.5 and 0.3 have a total ...
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16 views

Modern Linking Algorithm for Multi Period Performance Attribution

I'm looking for a modern description of the linking algorithms used in industry arithmetic performance attribution across multiple periods. Since the sum of the active return components in arithmetic ...
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3answers
141 views

How to calculate standard deviation of continuously compounded four-year stock returns?

Currently I am preparing for quant interview and I encounter the following question in Heard on the street. Question: If the standard deviation of continuously compounded annual stock returns is $...
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9k views

Annualzing the log of daily returns riddle

Two popular ways to measure returns are Arithmetic returns and Log returns. Let's define arithmetic (simple period) returns as: P(t) - P(t-1) / P(t-1). Let's define log return as Ln( P(t)/P(t-1) ) or ...
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2answers
121 views

Returns and logreturns differences

I have a time series of stock prices and I tried to calculate simple returns and log returns. However, I end up that simple returns has positive mean, but log returns has negative mean. Is it possible ...
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69 views

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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1answer
65 views

Derivation of the formula for $m$ compounding periods per year: $(1+\frac{i}{m})^{mt}$

A dollar return with interest $i$ invested for $T$ years with compounding interest frequency of $m$ times each year is: $$1*(1+\frac{i}{m})^{mt}.$$ My Question Why do we divide $i$ by $m$? Is this ...
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154 views

Distribution of simple returns vs logreturns

I understand that stock prices are conditionally modeled using a log normal distribution by the relationship $ y_t/y_{t−1}∼logN(μ_{daily},σ^2_{daily})$ $y_t∼logN(log(y_{t-1})+μ_{daily},σ^2_{...
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1answer
151 views

Rate of Return Required on Buying Stocks with Loan

A bank gives a loan $L$ for $m$ months and the monthly interest rate is $i$. The bank requires monthly installments - which I calculate is $I = \frac{L}{m} + Li$. I use this loan to buy stocks....
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39 views

How to deal with intermittent NA values in a price series when calculating returns

Let's say a have a price series for a share for the year 2000. On the 27th of July 2000, there is a missing value represented by NA. This was not a holiday or any other non trading day as other shares ...
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2answers
82 views

How are returns on Bond Funds (or ETFs) calculated?

For example, if we consider the fund "iShares Core U.S. Aggregate Bond ETF (AGG)", I am trying to figure out how the yearly/Monthly returns are being calculated. I extracted the historical NAV values ...
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Carry Trade vs synthetic Carry Trade using forward contracts

When it comes to foreign exchange carry trade strategy, the definition is straightforward: an investor borrows 1 US-\$ in the US (low interest country) and invests that \$1 to AU (high interest ...
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1answer
65 views

Efficient Frontier Graph

I'm writing some C code to create different portfolios using a few stocks that are given as inputs. I am having some trouble trying to find if these results are correct. My biggest hesitation is that ...
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1answer
37 views

Convert arithmetic returns to log returns [closed]

I have a series of arithmetic returns and I need log returns. I do not have the underlying prices. How do I convert? All the posts I have found explain why using one versus the other is appropriate ...
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1answer
74 views

How to calculate standard deviation cone around expected returns?

I would like to evaluate the returns of an investment manager who has given me their return and volatility expectations for their fund. I would like to calculate both 1 and 2 standard deviations from ...
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4answers
283 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 ...
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1answer
62 views

Portfolio & Asset Returns across Multiple Periods

The stocks of CK Tan's, Robertson's, and Tamashimaya are held by the hedge fund SSK. They hold an equally weighted portfolio. The end-of month prices of the stock during five months this year is given ...
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1answer
223 views

Return Contribution for Annual Returns

I have a portfolio $p$ made up of a bunch of assets $i$ where the weights change slowly over time. The returns over each period $j$ composed of the weighted returns of the asset $r^j_p$ $$ r^j_p =...
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1answer
29 views

Does Adjusted Closing Price take account the Expense Ratio?

first time posting at Quantitative Finance. I am trying to use the yfinance python library to load various ETF's data and compared the return. I understand the adjusted closing price handles the ...
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45 views

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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4answers
149 views

CAPM - Expected vs. actual returns

I'm trying to calculate alpha in excess of CAPM and have seen a few slightly different calculations for CAPM. The primary difference I am seeing is that some equations use expected market returns (e....
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1answer
50 views

EONIA capitalisé jour tr eur: can't find index data! Do you know what kind of index is?

To get EONIA capitalisé jour tr eur index returns (monthly returns from 01/2007 until the most recent) is challenging. First i googled the index name searching for the ISIN or the index provider ...
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1answer
78 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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1answer
84 views

How to calculate the daily rate of return for an actively traded account

I have a spot currency exchange account where the base currency is USD and where I can deposit and/or withdraw money from the account in any currency at any point in time. I can also exchange any ...
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1answer
76 views

Jensen’s Inequality for returns on short positions

this is puzzling me. Say you have an asset A, that on day t+1 returns 1%, and then on day t+2 returns 1% again. If you invest $1 in A on day t (take a long position), then on day t+2 you have earned:...
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What is the difference between Rolling Returns and Moving Average and how to calculate them?

So I understand what a moving average is and how to calculate it. I'm using this numpy function for it. I am somehow confused about how to calculate rolling returns. Different sites explain it ...
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83 views

Is it possible to compute implied returns from volatility?

If we assume that, broadly speaking: Assets in liquid markets are fairly priced to its value Volatility is predictable (volatility clustering, GARCH, etc) Investors are rewarded and earn a return for ...
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10answers
18k 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?
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38 views

Why do these Monthly vs. daily plots differ?

I got my data from Thomson Reuters Datastream. As an Input for my plot i calculated daily Returns based on the Return-Index provided by datastream. Then i plotted the Monthly and the daily Returns.(...
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1answer
173 views

Squared returns and volatility

Squared returns are considered pillars of GARCH/ARCH modelling and most used method for forecasting or studying volatility. Can you tell me how to calculate it from simple stock price. Is it better ...
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0answers
69 views

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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1answer
65 views

Portfolio return with changing assets over time

I need some feedback on a very basic question regarding the calculation of the portfolio return. I have created an example of a portfolio with two assets and attempted to calculate the return: I've ...
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2answers
90 views

How to calculate necessary gain to compensate a loss in a financial transaction?

(Feel free to suggest the correct Stackexchange community - or otherwise - if this is not the correct one) When trading financial markets, a gain of x%, won't ...
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1answer
2k views

How to compute simple and log portfolio returns?

I am looking for more details to perform simple and log returns for an entire portfolio. However, I've only been able to find the following semi-reliable source (see Page 9 and Page 19): Here are my ...
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1answer
2k views

How to convert Jensen's Alpha from monthly to quarterly observations

I am being puzzled while calculating jensen's alpha for single stocks. I have monthly returns data and have calculated alpha for each stock on a monthly basis (used 36-month rolling window for beta ...
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0answers
43 views

Calculation of IRR Given Stage Assumptions

I am trying to replicate Union Square Ventures Fund #1 model. A number of assumptions are given and the outcomes are listed. I have copied these into google sheets. I am not sure exactly how IRR is ...
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2answers
97 views

Why can we assume that asset return rates are normally (or lognormally) distributed?

In many theories of financial mathematics it is assumed that asset return rates are normally distributed (e.g. VaR models) or lognormally distributed (e.g. Black-Scholes model). In practice, asset ...
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0answers
34 views

Are the returns in this regression signed returns?

In this paper about combining multiple alphas are the returns signed returns? if not wouldn't they be mean zero? Also, it mentions "realized alpha returns" - does that just mean "realized" past alpha ...
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2answers
184 views

Cumulative Return on Futures

In my current backtesting, I am using log returns as a proxy for simple returns via the relationship $\ln(1 + r) \approx r$ for small enough r. This gives me wonderful properties like time additivity, ...
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0answers
23 views

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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1answer
50 views

ETF performance/returns

I was going over some ETF return data on yahoo finance and encountered some numbers that did not make sense to me. The image below shows a ytd return of 17.94% and 13.52%. I checked ETF.com and ETFdb ...
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55 views

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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1answer
58 views

Proof that IRR(A) < IRR(A+B) < IRR(B) ? Ie that the IRR of two cashflows together must be within the range of the IRR of the two cashflows?

The question The IRR of two sets of cashflow is not (necessarily) the weighted average of each set of cashflows. E.g. if ...
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1answer
76 views

Should the sum of daily returns be close to monthly returns

I am calculating value-weighted returns with monthly dividends reinvested and for some reason when I sum the daily returns some are a little bit off with monthly returns. Is this normal?
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1answer
115 views

Convert Geometric Direct Alpha PME to Arithmetic Excess IRR (PME Alpha / Implied Private Premium)

As a followup to this old question, Private Equity: Direct Alpha vs Excess IRR, I have a new one. In automating PME calculations, the Direct Alpha (DA) approach is computationally simpler and ...
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1answer
174 views

What is the correct way to calculate the annualized returns from rolling windows starting from monthly returns?

What is the correct way to calculate the annualized returns in 5-year rolling estimation windows starting from monthly returns? Is it most correct to first annualize the returns (using the geometric ...
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0answers
66 views

Logic behind calculating a Carry Multiple associated with Startup Valuation [closed]

I'm reading a book called "The #1 Guide to Startup Valuation: How to value your startup in 12 easy steps" (p. 22-23) by Joachim Blazer. As one of the building blocks, namely "Return", the Carry ...
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49 views

Possible application of Polya's Urn on Portfolio's Investments?

I wanted to find some more information of this topic, but I found very little. I might be interested in optimizing a stock investment portfolio. Maybe I could use beta or some other common risk ...