8 votes
Accepted

Are asset return means difficult to predict because they have no lower bound?

To answer, the assertion that volatility is easier to predict than expected return requires clarification. The phrase "easier to predict" is particularly ambiguous. To me this means that the ...
RRL's user avatar
  • 3,650
7 votes
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How to perform cross-sectional asset pricing regression?

I prefer thinking in terms of well measured vs. poorly measured rather than significant vs. insignificant: arbitrary p-value cutoffs and ignoring sensible priors can both be problematic. On the ...
Matthew Gunn's user avatar
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6 votes
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Expected return on Black-Scholes priced option?

We can obtain a closed-form solution for the expected return over an arbitrary holding period under some typical assumptions. Assuming geometric Brownian motion with drift $\mu$ and volatility $\sigma$...
RRL's user avatar
  • 3,650
5 votes

How to calculate the expected stock returns for an individual stock?

One of the best ways I came across to estimate the expected return of a stock (even with limited time-series data), is Martin and Wagner (2019): What is the expected return on a stock?. From their ...
phdstudent's user avatar
  • 8,306
5 votes
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What are the assumptions in the first-stage of Fama-MacBeth (1973)?

The CAPM is an economic theory that expected returns in excess of the risk free rate should be linear in the regression beta on the market. $$ \operatorname{E}[R_i - R^f] = \beta_i \operatorname{E}[R^...
Matthew Gunn's user avatar
  • 6,944
4 votes

Intuitive explanation of geometric mean

For a simple example, say you start with \$100 in an account. In the first year, it makes 50% gain (+50% interest) => \$150 In the second year, it makes 50% loss (-50% interest) => \$75 The ...
gdlamp's user avatar
  • 196
4 votes

How can risk-neutral pricing find the right price for securities if it doesn't account for risk premia?

The price of a derivative does not explicitly depend on the expected return of the underlying, however the price change or return of the derivative depends on the return of the underlying. Hence the ...
Kiwiakos's user avatar
  • 4,337
4 votes
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Methods for superior estimates of returns in m.v. portfolio optimization

Expected returns are very difficult to estimate reliably without incurring estimation error as found out by Merton (1980) "On estimating the expected return on the market". This is why estimating ...
develarist's user avatar
  • 2,990
3 votes
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What should happen to the equity risk premium as rates change?

There does not seem to be a clear relationship between interest rates and equity risk premiums. Damodaran (2019) has a great paper that goes into details of equity risk premiums. In this work, he ...
AK88's user avatar
  • 1,840
3 votes
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Proof of the convexity adjustment formula

Well, you need to know what is the stochashtic model you are using for $y_T$, if you assume it's a geometric brownian motion you have this process : $y_T = y_0 e^{\sigma W_T - \frac{1}{2} \sigma^2T} $...
user30150's user avatar
3 votes
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Expected option return in MATLAB

Under GBM $$ \frac {dS_t}{S_t} = \mu dt + \sigma dW_t $$ we get $$ S_T = S_0 e^{(\mu - \frac{1}{2}\sigma^2)T + \sigma W_T} $$ suggesting that $$ S_T \sim \text{ln}\mathcal {N} ( \tilde {\mu}, \tilde {\...
Quantuple's user avatar
  • 14.6k
3 votes
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Implied Expected Stock Return from European Option Prices

Note that \begin{align*} \frac{S_T-S_t}{S_t} &= \frac{S_T-K +K-S_t}{S_t}\\ &=\frac{(S_T-K)^+-(K-S_T)^+ +K-S_t}{S_t}. \end{align*} Then, \begin{align*} E\left(\frac{S_T-S_t}{S_t} \mid \mathcal{...
Gordon's user avatar
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3 votes

Where to find good notations to teach investment portfolio maths?

Financial markets & Corporate Strategy - Grinblatt & Titman The book is very intuitive, but as a consequence less comprehensive than ex. Options, Futures, and other Derivatives by Hull (which ...
dms_quant's user avatar
3 votes

Expected returns for scalping futures

Renaissance Technologies averaged 66% a year since 1998. The worst funds will lose all their capital and then some. A small time investor like you can expect to make not more than than buy and hold ...
Bob Jansen's user avatar
  • 8,552
3 votes

The Education of a Speculator - Gambling the Vig

I tried a MonteCarlo simulation with 10000 iterations and it seems to confirm a probability of about 0.0033 However I wonder if we are interpreting the problem correctly, we are assuming infinite ...
nbbo2's user avatar
  • 11.2k
3 votes

Measuring expected returns

When using arithmetic returns the right way to calculate an average is via the geometric average. The reason is that there is a multiplicative relationship between the returns. Example: Let $P_t$ ...
Count's user avatar
  • 491
3 votes

Fama French Factor adjusted returns

Yes. In a nutshell, the alpha of that regression will tell you how much of the portfolio expected return is not explained by the Fama-French 3-factor model and the $R^2$ of the regression will tell ...
phdstudent's user avatar
  • 8,306
3 votes

Why are long 2 year Treasury futures (ZT) trading at negative carry?

That's like saying, when the curve is upward sloping, why is anyone ever short ? Also, futures don't have carry, only roll down by definition. Carry pnls for cash are realised if fwds are realised - ...
user68819's user avatar
  • 395
2 votes
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Where to find good notations to teach investment portfolio maths?

If I had to give only one title this would be it: FT Guide to Understanding Finance by J. Estrada (Second Edition published 2011) It explains all of the above concepts (and more) in a very ...
vonjd's user avatar
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2 votes

Interpretation of Excess Return

They are both excess returns even though the standard convention is to talk about risk premium for $R_{t+1}-R^f$ and excess return on the market for $R_{t+1}-R_M$. If you believe in CAPM, then you ...
fni's user avatar
  • 1,886
2 votes

Derivation of arithmetic variation of a portfolio over multiple periods

$\newcommand{\E}{\mathbb{E}}$ $\newcommand{\V}{\mathbb{V}}$ First note that \begin{eqnarray} \E[(r_{t + n} + 1)^2] &=& \E[r_{t+n}^2 + 2r_{t + n} + 1] = \E[r_{t + n}^2] + 2\mu + 1 \\&=&...
caverac's user avatar
  • 311
2 votes

Questions on continuously compounded return vs long term expected return

There are two communities that parametrize the random variables of the returns and levels differently. And unfortunately, they both use the same notation. One community uses $\mu$ to denote the mean ...
Taylor's user avatar
  • 544
2 votes
Accepted

Why do surprises in macroeconomic variables average out to zero?

Your confusion is probably caused by these two facts: In theory, a surprise is descirbed by a random variable with so-called standard normal distribution having standard variation equal to zero. This ...
Martin Vesely's user avatar
2 votes

Expected returns for scalping futures

Note that your buy and hold returns of 25% are extremely atypical, partly because you started at a very good time (right in the middle of the credit crisis so you missed the majority of the 2008 ...
Chris Taylor's user avatar
  • 5,901
2 votes

Are asset return means difficult to predict because they have no lower bound?

The essential difference arises not from the lower bound on volatility, but rather the fact that volatility is mean-reverting and asset values are not. To make this clearer, note that a period-$T$ ...
Brian B's user avatar
  • 14.8k
2 votes
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relation between risk averson coefficient and maximum Sharp ratio in Black-Litterman context

Solving it algebraically: As seen in the above provided reference (just above " 1) "), the general formulation for the unconstrained Markowitz portfolio optimization scheme, is given by: \...
Pleb's user avatar
  • 4,276
2 votes

Do all risky assets have negative expected return over long enough time horizons?

Short answer [the link/URL doesn't work]. In a world without risk premia, this logic would be correct. Variance drag would cause all volatile risk assets to have negative expcted returns. Which is ...
demully's user avatar
  • 5,061
2 votes
Accepted

Return forecasting for portfolio optimization

I want to understand why factor models such as FF- 3-factor model are not used in practice for estimating the expected returns and covariance matrix (or different estimates given the inputs required ...
Richard Hardy's user avatar
1 vote

Should the targeted rate of return stay the same regardless of the currency?

Point of clarification : are you asking about required returns in pounds sterling for projects conducted in the UK? If so, you also need to adjust for any difference in risk free interest rates ...
dm63's user avatar
  • 17.1k
1 vote

Should the targeted rate of return stay the same regardless of the currency?

It depends. Is the project being carried in the original place or moving to the UK? If the project keeps being in the original place (i.e. euro zone) and you want the IRR in GBP, then you need ...
phdstudent's user avatar
  • 8,306

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