# Questions tagged [risk-free]

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### Risk free rate must be lower than expected return of global minimum variance portfolio

I heard a professor say: "We know the return of the risk free asset must be less than the expected return of the global minimum variance portfolio, otherwise there would be arbitrage ...
71 views

### Understanding risk-free discounting with fractional powers

Introduction Discounting a value $X_{T}$ is premised through the presence of a risk-free security with a rate of $r$ per annum that yields the same value at time $T$, in years. That is \begin{align*} ...
69 views

### Determine expected geometric return from Sharpe ratio

I'm trying to calculate the expected annual geometric return, given that I'm provided with an annual Sharpe ratio (0.5), the yield on a 3-month T-Bill (5%) (using this yield as a proxy for the risk-...
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### Filipovic: Where is it used that the world is deterministic

In this text (Damir Filipovic, Term-Structure Models, Springer, 2009) $P(t,T)$ denotes the price of a zero-coupon bond at time $t$ with maturity $T$. I cannot see where the proof uses the ...
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### Risk-free yield curve creation for Euro

I'm working on a Interes Rate Risk in Banking Book model for EVE calculation. It doesn't matter if you know what it is or not, I just need help with one step. That step is the creation of risk free ...
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### Calculating Risk Free Interest Rates for VIX formula

This question pertains to a whitepaper published by the CBOE that explains how the VIX index is calculated. Near the bottom of page 5 of the whitepaper, it explains that two risk-free interest rates ...
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419 views

### Which Risk Free rate to use?

I am trying to value a food and beverage company using DCF. I have forecasted the short term projections for 10 years and calculated a terminal value there after. But I am confused with which risk ...
65 views

### Portfolio optimisation

I want to create optimised portfolios in five different countries and calculate if the inclusion of cryptocurrencies or other alternative assets contribute to the diversification. I want to use ...
204 views

### Matching periodicity Fama-French Factors, Portfolio Return and Risk Free rate

I am trying to replicate certain aspects of the following paper: "Does the stock market fully value intangibles? Employee satisfaction and equity prices" - Alex Edmans (2011) for three ...
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### Market consistent valuation of a pension scheme with return smoothing

Assume we have an insurance company that is valued under a risk-neutral probability measure. Further assume that the company, for simplicity, only has return smoothing based insurance. Assets return ...
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1 vote
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### SOFR - calculation of the volume-weighted median and percentile

Federal Reserve Bank of New York web page provides some information on the computation of the SOFR rate. Part 1 According to this webpage, the SOFR is calculated as the volume-weighted median: "...
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### Which risk-free rate to use for the UK?

I am working on an assignment to calculate Beta in the CAPM Model through empirical data on the british market and am still unsure which risk-free rate to use. Since I have a 1 week investment horizon,...
107 views

### Physical Probability Measure vs. Risk Free Probability Measure (State Contigent Claims)

currently I am working on a problem regarding state contingent claims. I have 5 securities (one of the security is a risk-free security) and in the next period, these securities will end up in one of ...
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### how to use SOFR as risk free rate in portfolio construction

Good afternoof to everyone. I would like to create a portfolio following a multifactorial approach (I have been writing my master's thesis). As I would like to calculate a series of ratios (e.g. ...
1 vote
50 views

### How to link market risk and the transition to the new risk-free rates?

I'm a market risk analyst intern and I've the opportunity to do a project related to it. So I would like to move towards SOFR and €ster transitions, I have seen quite a lot of documentation on this ...
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1 vote
339 views

### Portfolio selection with no risk-free asset

Can someone explain why some papers on portfolio construction assume that there is no risk-free asset? For example, this paper: Machine Learning and Portfolio Optimization. What could be the reason(s) ...
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### What is the distribution of the risk-free asset?

If the risk-free asset has a volatility of $0$, therefore making its mean equal to the risk-free rate, $r_f$, does this mean that it has no probability distribution, and therefore there is no reason ...
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### USD MultiCurve Calibration - IOER vs. OIS/Fed Funds

I'm building out a calibrated USD MultiCurve set, focusing on Fed Funds & 3M LIBOR for the purpose of trading in Fed Funds Futures and Eurodollar Futures (for now ...). I had always assumed that ...
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1 vote
1k views

### What is the standard risk free rate used to discount options?

Apologies if this has been asked before - but I wanted to clarify what the market standard was for discounting options i.e. what is the "risk free" rate actually used by quants and traders? I haven't ...
1 vote
318 views

### What should I use as a proxy for the risk-free rate? And how do I transform the yearly risk-free rate to the weekly risk-free rate?

In order to calculate the Sharpe Ratio, I need the risk-free rate. What is the most convenient proxy for the risk-free rate? And how do I transform the yearly risk free rate to a weekly risk free rate?...
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5k views

### Overnight Index Swaps (OIS) vs. Fed Funds Futures

When calculating the probability of a certain target rate specified by the Fed at an FOMC release, I’ve generally read that it is typical to use Fed Funds Futures as proxies. I can find data on this ...
645 views

### T-bond of what maturity to use as risk-free rate when calculating excess return?

I am comparing different asset classes in order to estimate the expected return and the risk of a portfolio. I have historical data (adjusted close price) for my asset classes for the last 5 years ...
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### Is EONIA swap rate really credit risk free?

I have a question linked to the EURIBOR – EONIA spread (or OIS LIBOR spread). I understand that the EURIBOR - EONIA spread is a credit risk indicator of the interbank market. There is something I ...
423 views

### Proof that we can price any derivative as the discounted value of its expected return under the risk neutral measure

I am reading a paper which tries to convey the intuition behind the Black-Scholes pricing formula. In that paper, the author states the following two things without proof, and I would like to know why ...
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### Which rate to use as a risk free rate in emerging markets?

By looking at Fama and Frenchs global Portfolios, they just use the USD-RF rate as the risk free rate, because they converted their Returns to US-Dollar. Im currently estimating Strategy Returns in ...
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### Why use the risk-free rate for discounting in a risk neutral world?

I am reading Options, Futures, and other derivatives by John C. Hull. In the chapter on Binomial trees, he remarks: A risk-neutral world has two features that simplify the pricing of derivatives: ...
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1 vote
262 views

### How to find the tangency portfolio using quadprog in R with different risk free rates

I am trying to find the optimal tangency portfolio for the efficient frontier (calculated using qp.solver in quadprog) but subject to different risk-free rates. Demos for quadprog in R show that to ...
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2k views

### Which proxy is the best to calculate daily risk free rate for a capital asset pricing model?

I need to get daily risk free rate to measure my capital asset pricing model. However, I am still confused on which proxy to use for that (my sample comprises German stocks). Some empirical studies ...
1 vote
807 views

### if the​ risk-free interest rate​ increases, and nothing else changes, is the market portfolio still efficient?

I think the response is no but I don't know why If so, Stocks with betas greater than one will be buying opportunities and stocks with betas less than one will be selling opportunities because I can ...
611 views

### Why we can't lower a volatility of a portfolio (without changing expected return) by substituting a zero beta stock with a risk free asset?

part of the answer is that a zero-beta stock must be negatively correlated with other stocks in the portfolio. So having a zero beta stock can decrease the volatility. Does that mean that the ...
862 views

### Risk aversion and risk-free rates

New to finance. When I read textbook like Financial Economics by Bodie, I encountered the following idea, namely, higher risk aversion is associated with higher risk premium and lower risk-free rate. ...
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217 views

### CAPM: Bond index as proxy for Rf

Is it possible to use a bond index as a proxy for Rf in CAPM? Please let me know what is the issue here.
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### Why can a deterministic portfolio only grow at risk free rate

In black scholes derivation we assume that portfolio grows at risk free rate because the process is deterministic, my question is why is it riskfree rate? If i have information about some event in the ...
176 views

### What is considered the risk free rate? [closed]

I see some place reference the S&P 500 index (SPY) as the risk-free rate and other place reference the 10-year Treasury yield as the risk-free rate. Which one is the correct one?
1 vote
2k views

### How does a Delta Hedged portfolio yield the Risk-free?

Here I'm considering the simple case of a dealer writing call options on a stock and hedging the short position with a "textbook" Delta Hedge, i.e. goes long on $N_c \times Delta$ stocks (where $N_c$ ...
411 views

### option call question

i have a question regarding a call option exercise i cant get my head around The price of a stock is 100, the continuously compounded risk free rate is 5%. The strike price of an european call option ...
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### How to work out bond price given other bond prices?

I'm stuck on the following problem from a financial maths course, and was wondering whether anybody would be able to help me. I don't really know where to begin. The following risk free bonds are ...
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### Calculating the Risk Free Rate [closed]

I have an assignment and I have to calculate the risk-free rate with the following data: Stock A: E(R) = 10% ; Standard Deviation = 5%. Stock B: E(R) = 20% ; Standard Deviation = 10%. I also ...
1 vote
146 views

### How to correctly use SharpeRatio.annualized function with daily returns and proxy for daily risk free rate

I am not sure if am correctly using SharpeRatio.annualized function. I am passing following parameters (dailyRet, dailyRF, scale = 252), where dailyRet is an XTS type for daily returns, dailyRF is an ...
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732 views

### daily risk-free rate proxy

3-month or 1-month Treasury bill yields are typically used as proxies for the risk-free rate. However, it is often the case that - especially for developing economies - that data is only available at ...
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### Drift rate vs. Riskless rate in the Black-Scholes model

I'm teaching an applied math class this summer and I want to take a short detour into finance (not my specialty at all); specifically the Black-Scholes model of stock movements. I want my students to ...
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### Why do we discount in ois and not treasuries

OIS is the 1-day non-collateralized interbank interest rate. Such a rate is not risk-free. The market trades a very useful curve that is much closer to "risk-free": the government bond curve. So the ...
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### How to determine the risk free rate for the calculation of Beta

I want to calculate the beta of a computer vendor using return data from 31st Jan 2008 to 31 Jan 2013 (period of five years) against the return of S&P500. I will be regressing the excess return ...
1k views

### Why must the risk free rate be free from risk in risk neutral valuation?

I am reading through documentation related to Funding Valuation Adjustments (FVA) which discuss risk free rate and funding matters and the following question came to my mind: in risk neutral valuation ...
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1k views

### Sharpe Ratio, risk free rate [closed]

when comparing the Sharpe Ratio (SR) of two different funds, does it make a difference, whether I use excess returs (returns - risk free rate) or returns (without dedcuting the risk free rate, ...
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### Portfolio with several risky assets and one risk-free

Suppose we have $N$ risky assets $r_1$, $r_2$, ... , $r_N$ with a covariance matrix C. If we want to build a portfolio $\omega = (\omega_1, \ldots, \omega_N)^t$ (I loosely denote the portfolio with ...
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### Is there any public data to get OIS for differal time (1d, 1W, 1M, ..., 10Y)?

I want to get data of Overnight Index Swap, also known as OIS rate, there is any public why to get this always from yesterday? For example, I want to get EFFR(Effective Federal Funds Rate), I can get ...
10k views

### how to calculate daily risk free rate using 13 week treasury bill

I want to calculate excess return for AAPL plus the S&P 500. I have computed monthly and daily logarithmic returns for every stock and for the market, I now need to calculate the risk free ...
We have $dB_t = rB_tdt$. We are told that this corresponds to a "bank"..... how? When I insert money into a bank, how does this correspond to buying an asset for the price $B_t$? It would make more ...