# Questions tagged [compounding]

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### Modeling compounded RFRs with Vasicek

I’m wondering if simple interest rates models, like Vasicek, could be successfully used for modeling compounded setting-in-arrears rates (compounded SOFR for example)? As far as I see I can do that ...
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### Periodic investments with compound interest: where's the mistake?

Consider two investment strategies: Every year, I have a quantity $I_a$ to invest. There is a financial object that gives an anual return of $r$, that is, after a year it transforms $I_a \mapsto rI_a$....
47 views

### compounding in short positions

Why does compounding doesn't work in short positions? Let's say I have following mini time series 5 6 4 2.5 Returns are -20%, 33% and 37.5%. So compounding return equals to 46.67% = 0.8 * 1.33 * 1.375....
36 views

### Sharpe ratios (and other risk-adjusted metrics) on Terminal wealth (long-horizon payoffs)

I'm exploring financial simulations with bootstrapped returns (TxNBoot) to calculate long-horizon returns. Terminal wealth (e.g compounded returns at T) is a vector of payoffs (NBootx1), typically ...
91 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 vote
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### 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 ...
• 1,474
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### Applications of a certain type of stochastic processes in quantitative finance [duplicate]

A compound Poisson random vector $Y$ is well defined in this site in wikipidia. Nothing prevents me from compound strictly stationary stochastic processes instead of compound random vectors. The ...
102 views

### Monthly and annual arithmetic mean in valuations? [closed]

I know this is back to basics but I am perplexed by it!!! Assume that the future value (FV) of an investment at the end of year 1 is 112, the annual arithmetic expected return is 12%, hence the ...
1 vote
411 views

### Day Count Convention & Compounding Frequency Assumption in Interest Rate Swaps and Discount Factors

This question concerns old LIBOR Swaps where their fixed legs are based on 30/360, and floating legs on Act/360. Q1. Let's assume the simple self-discounting case where spot rates are obtained ...
74 views

### How should we interpret r_c in continuously compounded interest? [closed]

I'm just curious there is any useful "meaning" or interpretation we can assign directly to $r_c$. Of course one can directly calculate the non-continuously compounded interest from $r_c$, ...
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1 vote
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### Quantlib Yield curve and rate compounding [duplicate]

I need help in understanding Quantlib's interpretation of yield curve and rates. The rate output retrieved from yield curve differs from expectation for non continuous cases. Illustration: Let's start ...
237 views

### equivalentRate not matching for compounding cashflows

I am calculating equivalentrate between two days in quantlib python using following functions but the output is not matching with the manual calculation. ...
251 views

### compounding component contributions

Say I have a portfolio which contains two components, A & B. Below are the daily contributions to performance (0.02 equals 2%), where the overall portfolio return is equal to the sum of component ...
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### How to calculate the number of stocks I can buy with X dollars, if we know the exact growth rate of the stock price per dollar?

Let's say we have a stock whose price goes up at a rate (from the doubling time formula): $r = e^{(\text{volume}/1000 * \ln(1.2))} - 1$ (The 1 is subtracted from e^pwr, not from pwr) Meaning that it ...
• 135
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### Intuition behind reasoning around interests-in-advance

I quote Life Insurance Mathematics (Gerber, 1997). Let $i$ be an annual effective interest rate and $d$ an annual effective discount rate. In case of interests-in-advance, a person investing an ...
151 views

### Why continuously compounded interest a standard in finance? [closed]

Why is the "continuously compounded interest" the standard in finance? Many finance textbooks use the formula e^rt without justification. The assumption that the interest frequency is ...
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### Kelly fraction for discrete distributions

The Kelly fraction is $f^\star$ maximizing $\mathbb E[\log(1+f X)]$. For instance, if $$X\sim\begin{cases} 1 & w.p. p\\ -1 & w.p. 1-p \end{cases},$$ we get that $f^\star=2p-1$. I'm curious ...
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### How do you simulate returns for a portfolio when you have Lumpsum + Monthly investments (SIP) in place?

I'm trying to simulate portfolio returns using Norm.inv function in excel. Inputs to the formula: Prob= Rand, Std dev= Historical, Mean= 5 year historical average. Its easy to do this when you're ...
• 11
345 views

### Using Quantlib to pricing a FR007 swap (which is compounding interest rate in floating leg)

You can treat the FR007 swap like this: The fixed-rate leg is the same as the fixed-rate leg of the LIBOR swap. The floating rate can be treated as the combination of some 3-months maturity compound ...
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300 views

### Why different compounding in interest rates

This is more a philosophicalquestion than a financial question, let me explain. There exist different types of interest rate (Annual Interest rate, Semi-annual interest rate, monthly interest rate, ...
• 179
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### Compounding Equivalence

I am trying to understand under what circumstances or transformations would $[1+(E_2-E_1)*\frac{d}{360}]$ equal to $(\frac{1+E_2}{1+E_1})^{\frac{d}{360}}$. For context, $E_2, E_1$ are interest rates. ...
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579 views

### PV of the Floating Side of an "Overnight Index Swap" (at the fixing Date)

I have a mathematical / theoretical question regarding the PV of an Overnight Index Swap (Floating Side) at the time of fixing. Starting from this question: How to compute Overnight Index Swap (OIS) ...
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### Properties of difference between continuous and discrete compounding of interest rate [closed]

The relationship between annual discrete and continuous compounding interest rates is given as: $$1+r_d = e^{r_c}$$ My question is what are the properties of the difference between $r_d$ and $r_c$? ...
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1 vote
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### Calculating coupon yield and continous compounding

I need to calculate the yield of a 2 year Coupon Bond. Price = 98, Coupon = 3.5, N = 100. Now when I try to solve this, I arrive at the equation: $$98 = 3,5*e^{-y}+103,5*e^{-2*y}$$ But I can't ...
860 views

### OIS fixed rate compunding criteria

I have the following doubt: How should the OIS fixed rate be considered in computing principal+interests at the maturity of the swap? I mean, if i.e. the swap lasts 4 day (without w.e. in the middle), ...
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1 vote
75 views

### Accrued interest on yearly compounded instrument after less than a year

I am reading a book on fixed income instruments and don't quite understand one of the examples on compounded rates. Let's say the investement is compounded yearly at rate $r$. Then after $T$ years, ...
• 113
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### Compound the monthly returns to make them quarterly [closed]

How can someone make the Kenneth French library data returns quarterly from monthly? Since they are not loq returns, then you need to compound returns rather than summing them up. I want to make the ...
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1 vote
896 views

### Calculating the daily continuously compounded return from index values

Given I have 3 index values at time $t = 0, 1 , 2$, how would I go about calculating the daily continuously compounded return? Time: $0, 1, 2$ Index Values: $4000, 4086, 4114$ Any help would be ...
• 133
514 views

### Why continuously compounding

Why are we compounding continuously in finance? I have searched around, but I cannot find an explination on why we actually do it. I assume that we, in theory, do it because every interest earned is ...
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1 vote
474 views

### Pricing of the compound coupon bond with PDE

I am now studying finance math using Steven E.Shereve's book. Using Interest Rate models, We can the price for zero-coupon with maturity price $1$ under Hull-White interest rate model[page 274] and ...
651 views

### Pricing of compounded swaps

As far as I understand, a compounded swap rolls up individual payments into one final payment which becomes: $$V(t_n) = N \prod_{i = 0}^{n-1}(1 + d_i L_i)-N$$ where $d_i$ is the day fraction for ...
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1 vote
105 views

### Custom benchmark construction (S&P500 + add-on)

If I have a strategy that has the same risk as S&P500 but also requires 150 bps on top of S&P500 Index, how would I construct such a benchmark? I have the following approach, but it is not ...
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### Interest rates compounded monthly [closed]

Suppose the quoted APR is $r_0 = x-1$ and interest is compounded monthly; Am I correct in saying the formula for the monthly interest rate $r$ is: $$r = (1+ (\frac{r_0}{m}))^m -1$$ Is it also ...
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1 vote
215 views

### Continuously Compounded rate less than a discretely compounded rate [closed]

I'm looking at an example in a well known book and its saying "consider an interest rate that is quoted as 10% per annum with semi annual compounding" The book puts 10% as the semi-annual rate, ...
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1 vote
220 views

### Can anyone explain to how Hull get from stock returns to continuously compounded stock returns?

I'm reading Chapter 13 of Hull's book and am stuck on how he got from stock returns to continuously compounded stock returns. As a recap, he built the generalized Wiener Process, which describes a ...
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1 vote
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### pricing of futures

When pricing futures with the cost of carry model; When do you use continuous compounding and when do you just use simple compounding? AND WHY? Also, when deriving proof of no arbitrage with the cost ...
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1 vote
536 views

### What is, here, the relationship between "compound" and "arithmetic return" and "volatility"?

I'm trying to find the exact (ie, not an approximate) relation between the "Compound Return", "Arithmetic Return", and the "Annualised Volatility" as given the assumptions below, and from there the ...
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86 views

### Compound 3-year returns to obtain 10-year returns: How to do?

I have 3-year returns at a monthly frequency, snippet below. How to compound the 3-year returns to obtain 10-year returns (since the cumulative product of 3 3-year return would be the 9-year return). ...
95 views

### reconciling arithmetic and geometric compounding

I have just been through 4 papers that make all sorts of clever claims about the 'alternate universes' of arithmetic returns and geometric returns, how thr twain shall never meet, and how they are ...
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1 vote
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### tenor basis swap spreads and compounding

Let's say I have a 3mv6m tenor basis swap that is quoted at a spread of x bp (and it is a spread on the 3m leg while the 6m leg is the flat leg). Nowadays, I think the convention in most currencies is ...
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1 vote
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### What is meant by the term 'unbounded compounding'?

I am currently trying to make sense of a paper by Mark Braverman and Kanika Pasricha titled "The computational hardness of pricing compound options". On page 3 of this paper, it claims that "With ...
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### Simple Compounding vs Continuous Compounding in return series

I'm creating a log price series in MATLAB. This is fairly easy to do using standard functions. Given a price series prices: ...
1 vote
560 views

### Characteristics of a Discount Curve

Does the discount curve used for discounting cash flows have to be a zero coupon, annual compounding, actual by actual day basis curve? In practice, does a curve used for discounting necessarily have ...
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### From continuous compounding to simple compounding - convexity adjustment

I have derived the convexity adjustment expression for futures rates using the Ho-Lee model, to arrive at the following: $$ForwardRate = FuturesRate - \frac{1}{2}\sigma^2T_1T_2$$ where $T_1$ refers ...
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1 vote
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### Compound interest calculator solving for time with deposits [closed]

I am attempting to solve a compound interest calculation for time given Principal = 100 Time(years) = t Rate(per year) = 8% Deposit(per month) = 5 Total = 300 I ...
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1 vote