Questions tagged [diversification]

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Literature about optimal number of stocks in a diversified portfolio

Is there any recent paper on how many assets one should consider for portfolio optimization techniques? I found: – https://www.jstor.org/stable/2330969?seq=1#metadata_info_tab_contents – https://...
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Why "hedging motives" and "heterogeneous preferences" are explanation for "under diversification puzzle"?

Han et al. 2021 documented something relating to the "under diversification puzzle": Standard explanations for under diversification include hedging motives and heterogeneous preferences, ...
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1 vote
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107 views

Herfindahl-Hirsch-Index for FX Portfolios

Assume we have an FX portfolio with $n$ currency pairs, such that $w_i$ is the weight of currency pair $i \in \{1, \dots, n\}$ in the portfolio, and $\sum_{i=1}^n w_i = 1$. All pairs have USD as one ...
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-4 votes
1 answer
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How to choose a stock? [closed]

So far, I have only been working on systems that track numerous stocks and evaluate which present the best opportunities at a given time. I have grown curious about building a day-trading system that ...
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2 votes
0 answers
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Do options have diversification benefit?

Imagine the universe where we have one investable volatile asset but with an available liquid options chain for it. The question: can a portfolio consisted of this asset, and some options have any ...
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0 answers
76 views

How to calculate if a portfolio has diversification

I writing a paper and wanted to know the best way, method or theory to know if a portfolio is diversified. To give you some context, I wanted to know if whether putting Bitcoin into a portfolio with ...
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0 votes
1 answer
42 views

Do equity mutual funds typically have industry-level diversification constraints? [closed]

For instance, are there limits to how concentrated a portfolio in terms of industry allocation? If so, where can I find such information about the constraints each fund has?
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2 votes
1 answer
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Which portfolio is more "diversified": the $\frac{1}{N}$, the MDP or the max decorrelation?

Equally-weighted portfolio: weights each asset the same $w_i = 1/N$ Maximum diversification portfolio: maximizes the ratio, $\frac{w' \sigma}{\sqrt{w' \Sigma w}}$ Maximum decorrelation portfolio: ...
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2 votes
1 answer
272 views

Non-linear correlation (co-dependence) and the efficient frontier

The graph below shows how the efficient frontier for 2 assets bends into a sharp bisection as correlation decreases from $1$ to $-1$, with $\rho=-1$ being the most diversified, and highly unattainable ...
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1 vote
1 answer
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Why is standard error used to show diversification effect for unsystematic risk?

quite long text incoming, sorry for that: While reading a corporate finance textbook, i came across a section describing the effect of diversification as well as the systematic and unsystematic risk. ...
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0 votes
2 answers
831 views

How can beta be negative? [closed]

I've been reading about the security market line and the definition of beta as $$\beta_i = \frac{Cov(R_i, R_m)}{Var(R_m)} $$ for any asset (doesn't have to be an efficient portfolio), and have read ...
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1 vote
1 answer
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Total portfolio VaR greater than aggregated individual VaRs

I am facing something weird in a simulation. I have calculated a portfolio VaR: 100\$. Then I aggregated the VaR for individual position (loans) and obtain: 98\$. I thought it was not possible for the ...
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2 votes
1 answer
73 views

Is there a sound logic for buying a portfolio of call options in the same ratio as you would buy the underlying shares?

Suppose I believe it would be profitable to build an investment portfolio by investing, say, USD 30,000 in stocks in the following ratio: 30% in shares of CompanyA, 30% in CompanyB and 40% in CompanyC....
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3 votes
1 answer
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how to construct a diversified portfolio based on correlation

I have a porfolio of indexes and I built up a python model based on spearman correlation (I used a spearman and not a pearson because, after running some test on outliers and normality ...
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1 vote
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Can simple risk management outperform portfolio optimization like this, or is there most likely an error?

I am using a simulation approach to compare the performances achievable by simple risk management and portfolio optimization for portfolio selection. My problem is that my results indicate that simple ...
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0 votes
0 answers
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Is time diversification effective?

If the returns are log-normal, how do I find the probability of negative returns, since log can only take positive values as an argument. Also, for time = more than 1 year, how do I find the ...
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1 vote
2 answers
102 views

Formula for underdiversification

I'm trying to develop a study which links a person's demographic and social characteristics to a tendency to under diversify their portfolio. So far I was accounting for risk aversion and just going ...
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2 votes
1 answer
117 views

Maximum Diversification Strategy without risk free asset

I am currently dealing with the Maximum Diversification Strategy and I am trying to understand the synthetic universe approach from Choueifaty et al.(https://www.tobam.fr/wp-content/uploads/2014/12/...
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3 votes
1 answer
247 views

Which Maximum Diversification Approach in MATLAB is correct?

I am currently trying to find the portfolio weights of the Maximum Diversification Portfolio and found two approaches which result in different outcomes. The first one is based on this paper:https://...
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4 votes
0 answers
149 views

Is Ledoit-Wolf Shrinkage with a Constant Correlation Prior Reasonable for a Stock/Bond Mix?

I've been looking into Ledoit-Wolf shrinkage but I've found the papers concentrate on large numbers of assets that tend to all be highly correlated. Often a universe of large cap stocks. I'm ...
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1 vote
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Magnitude of the Diversification Ratio

How would I interpret the magnitude of the Diversification ratio? I know that the higher the number, the better, but is 1.1 massively different that 1.2? For example a sharpe ratio of 0.25 is ...
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4 votes
1 answer
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Portfolio Allocation given Sharpe Ratio

If there are two portfolios with sharpe ratios of 1.2 and 0.5, what would be the allocation rationale. If the correlation between portfolios is: $a. 0 $ $b. 0.8 $ $c.-0.8 $ I see there is a ...
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16 votes
2 answers
7k views

Intuitive Explanation for Shannon's Demon?

I am reading Fortune's Formula by William Poundstone, and I am puzzled by a phenomenon called "Shannon's Demon", which Claude Shannon allegedly proposed in a series of lectures, and preserved only by ...
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0 votes
1 answer
170 views

Is it better to express a currency position through multiple pairs?

I use a trend-following approach where I look for trends in various currency pairs such as GBP/USD or EUR/USD and then take a position in the Spot currency. I measure the performance of my strategy by ...
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1 vote
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Zero-beta assets and the Sharpe-Lintner CAPM

I'm reading The Capital Asset Pricing Model: Theory and Evidence (Fama and French, 2004) and came across the following statement: "A risky asset’s return is uncorrelated with the market return—its ...
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2 votes
1 answer
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Decreasing dependence during the financial crisis?

In "Is the Potential for International Diversification Disappearing? A Dynamic Copula Approach" by Christoffersen et al. (2012), the authors present the concept of Conditional Diversification Benefit ...
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2 votes
0 answers
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$0$-beta stock and diversification

If we invest $w$ in the market portfolio and $1 - w$ in the risk-free asset, and observe a $0$-beta asset with expected return greater than the return on the risk-free asset, how can this be used in ...
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1 vote
1 answer
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How to measure if investors are diversified in a stock market?

My question is related to this question but it is not the same. Consider the US stock market. How can I tell if people trading in this market hold properly diversified portfolios? Is there some ...
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1 vote
2 answers
283 views

Value-at-Risk "hiding risk in the tail" and diversification?

I have a question regarding Value-at-Risk and diversification? When one says that VaR "hides the risk in the tail", does one mean that if we for instance look at VaR at level p=0.05 say, we might get ...
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1 vote
5 answers
413 views

What can I use to measure of diversification?

I have to come up with a measure of diversification for trade (this can tie in closely to diversification as regards portfolios). Are there any well known measures of portfolio diversification?
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2 votes
1 answer
53 views

Can adding an uncorrelated high vol strategy to a low vol portfolio result in a portfolio with even lower volatility?

Let's say I have fund A with 20% annualized volatility and portfolio B with 15% annualized volatility. If A and B have 0 correlation, can the combination of these funds have volatility < 15% ? Are ...
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1 vote
1 answer
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Risk minimization by investing in all assets with positive expected return

Suppose I have an amount $T$ to invest and $N$ available assets. The stochastic return per invested unit of asset $i$ is $R_i$. The variance and the expectation of $R_i$ are $\sigma^2_i$ and $\...
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3 votes
2 answers
527 views

Why does it "say" portfolio diversification not suitable during market turmoil?

Currently I am trying to get a hold of MPT, asset allocation and related applications. While reading a particular resource, it says diversification works best for "normal" financial markets and ...
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6 votes
1 answer
1k views

Is there any open-source library, implementing "exchange" to be used for algorithms running on the same computer?

Question: Is there any open-source project/library, which can act as a "local exchange" for agents (algorithms), running on the same computer? Clarification: by "local exchange" I mean, that the ...
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1 vote
1 answer
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How to adjust local currency returns to US$/EUR return?

Iam doing research on return characteristics. As of today the scope of the research has changed from a local investor point of view to an international investor point of view. This basically means ...
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1 vote
0 answers
497 views

Call options portfolio: what would the underlyings' moments to be maximized?

Let you have only three underlyings, like SPY, TLT and GLD, and you want to buy $n_{1}$ Call options on SPY, $n_{2}$ Call options on TLT and $n_{3}$ Call options on GLD... with a limited budget, that ...
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3 votes
1 answer
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Is this comment right about subadditivity?

I found this comment in a book I bought about risk management: Risk Management in Banking by Joel Bessis. This is the well-known rule that states that the sum of individual risks is less than the ...
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9 votes
2 answers
223 views

St Petersburg lottery pricing & short investing horizons

I am a statistician (no solid background in finance). Please forward me to a book \ chapter \ paper to resolve the following general question. Suppose we have a stock with the following monthly return ...
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8 votes
3 answers
423 views

age-sensitive correlation measurements in finances

When it comes to comparing returns or prices of instruments like stocks/ETFs, are there any well-established formulas, or ones in common use, that place stronger emphasis on recent correlations more ...
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4 votes
4 answers
829 views

portfolio diversification tester

Are there any online tools (optionally with developer API, to spare me the scraping) that given an existing portfolio, calculate how well a new candidate position would score to increase combined ...
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7 votes
1 answer
3k views

How to simulate correlated assets for illustrating portfolio diversification?

I have seen multiple instances where people try to explain the diversification effects of having assets with a certain level of correlation, especially in the "most diversified portfolio" literature. ...
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7 votes
3 answers
518 views

Should the average investor hold commodities as part of a broadly diversified portfolio?

Many mutual funds sell "asset allocation" products which include appropriately sized investments in a variety of asset classes meant for a prototypical investor. Some of these, such as PIMCO, even ...
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18 votes
3 answers
6k views

How do I find the most diversified portfolio, or least correlated subset, of stocks?

I have a trading system that chooses top 10 stocks in Nasdaq 100 ranked on relative strength and some other factors. However, I'd like to take positions in only 5 of these 10 stocks based on how ...
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20 votes
3 answers
2k views

How does one analyze diversification if stock prices follow a Cauchy distribution?

How does diversification actually lead to less variance in a portfolio? I'm looking for a formal reason why this is the case. There are a number of explanations I have been able to find, but they make ...
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5 votes
0 answers
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Benefits of Diversification and Rebalancing with negatively skewed leptokurtic return distribution?

I am missing tools to investigate this issue. I am trying to solve this question here. What kind of issues should you acknowledge over the naive diversification/rebalancing with normal distribution? ...
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