This document discusses using portfolio theory and utility theory to optimize the market mix of tourist origins for destinations. It presents research applying this approach to optimize France's portfolio of European tourist origins from 2007-2013. The portfolio model calculates the optimal proportions of each origin to maximize return for a given risk level based on growth rates, variances, and covariances. The results show France's current portfolio is sub-optimal with higher risk than optimized portfolios providing similar returns. Accounting for a decision maker's risk aversion allows identifying a preferred efficient portfolio to improve destination performance.

1. Perpignan University
Department of tourism
management
1
BOTTI Laurent
RAKOTONDRAMARO Hanitra
An ongoing research on the vector X
of destinations
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2. 2
1. Portfolio management applied to tourism
2. Vector X optimization and preference theory
3. Application to France with European tourists overnight stays
4. Limits and perspectives
Optimal market mix of destinations:
the case of France
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•Improve economic performance of destination /
heterogeneity between origins
•How to choose the best market mix?
•Markowitz (1952) (Modern Portfolio Theory - MPT) formulates
an approach allowing to solve the asset selection problem /
it figures out each asset proportion (i.e. weight, in
percentage) in the optimal portfolio (vector X)
1. Portfolio management applied to tourism
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•Some studies have highlighted how MPT can be applied to
optimize destination management
•Kennedy, 1998
•Useful to determine an efficient portfolio
•But unable to incorporate the decision maker risk aversion
(utility theory)
•Only 7 origins analyzed by considering Ireland as the
destination
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1. Portfolio management applied to tourism

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•Botti, Goncalves & Ratsimbanierana, 2012 (case of France) /
Ratsimbanierana et al., 2013 (case of Morocco)
•Used DDF in a MV framework to measure the destination
efficiency according to tourist origins / Measured the TE of
different virtuals portfolios
•Useful to determine an efficient (but virtual) portfolio / But
unable to incorporate the decision maker risk aversion
(utility theory)
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1. Portfolio management applied to tourism

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•Zhang, Botti & Petit (2016) introduced the utility function in
the MV space
• Used DDF in a mean-variance framework to measure the destination
efficiency according to tourist origins
• Measured the OE which can be decomposed into PE and AE +
introduced the decision maker utility function
• Did not focus on the optimal composition of the destination portfolio
 We use both portfolio theory and utility theory
 Calculate the optimal proportion of each origin
 Advice DMO to improve the performance of its destination
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1. Portfolio management applied to tourism

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1. Identify all combinations of origins that are MV efficient
2. Choose the efficient portfolio that is prefered given the
destination manager risk aversion
2 indifference curves (U1 and U2)
2 optimal portfolios (A and B)
DM 2 has a higher risk tolerance
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1. Portfolio management applied to tourism

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•The portfolio model requires 3 types of variables
(Luenberger, 1995):
•(1) the expected return of each asset in the portfolio (over
the period taken in consideration)
•(2) the variance of each asset’s return over time
•(3) the covariance among asset’s return over time
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2. Vector X optimization and preference theory

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•Expected return for a particular portfolio which includes 𝑁
assets with
• 𝑁 number of assets in portfolio p,
• 𝑋𝑖 proportion of the asset 𝑖 in the portfolio p
• and 𝑅𝑖 expected return of the asset 𝑖
•Variance for a particular portfolio with
• 𝜎𝑖𝑗 covariance between return of asset 𝑖 and return of asset
𝑗
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2. Vector X optimization and preference theory

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•Following Jang and Chen (2008), the MPT can be formulated
as follows for 𝑁 assets:
• 𝐶1𝑖 and 𝐶2𝑖 represent respectively
• lower and
• upper limits
• of 𝑋𝑖 (proportion of asset i)
2. Vector X optimization and preference theory
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•Three levels of risk aversion (𝐴) are taken in consideration:
• 𝐴 = 2
• 𝐴 = 3 higher level of A represents more risk aversion
• 𝐴 = 4
• The utility function can be written as follows with 𝐸 𝑅 expected
return and 𝜎2
variance of returns
2. Vector X optimization and preference theory
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•The optimum value of 𝑋𝑖 is computed by solving the
following quadratic program:
• 𝐶1𝑖 and 𝐶2𝑖 represent respectively
•lower and
•upper limits
•of 𝑋𝑖 (proportion of asset i)
2. Vector X optimization and preference theory
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•Number of inbounds overnight stays (usual KPI)
•Period from 2007 to 2013
•17 origins
•Corresponding proxies for the MV variables are:
•(1) average growth rates for each origin (expected return)
•(2) variance of each origin’s growth rates over time
•(3) covariance among all origins’ growth rates over time
3. Application to France
with European tourists overnight stays
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3. Application to France
with European tourists overnight stays
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•Some results of this optimization
• P0 is the current portfolio (2013)
• Expected growth of P0 and P1 are quite similar / risk associated to P1
is significantly less important than the one associated with P0
• P0 and P5 have a similar standard deviation / the optimized portfolio
P5 has a higher expected growth
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3. Application to France
with European tourists overnight stays

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•Current portfolio is sub-optimal
• Does not provide enough return for its level of risk
• It has a higher level of risk for its growth rate
•To reach the efficient frontier, decision maker should modify
the composition of its destination portfolio (depending on its
risk aversion)
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3. Application to France
with European tourists overnight stays

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•Rate of origin’s return is a random variable which can be
described by its mean and variance (?) / Variance is a
good measure of asset’s (origin’s) risk (?)
•Ability to change the market mix (?) Is there a decision
maker (DMO)? Risk aversion level? -> Fuzzy appreciation
•Lower and upper limits of proportion of origin i?
• Lower limit is the minimal proportion of origin i (during the
period) * 0.5 (Jang and Chen, 2008)
• Upper limit is the maximal proportion of origin i (during the
period) * 1.5 (Jang and Chen, 2008)
• Finding a DMO (a destination) on which applied the model
4. Limits and perspectives
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Thank you for attention!
laurent.botti@univ-perp.fr
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