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5th QATEM
Perpignan University Department of tourism
management
1
BOTTI Laurent RAKOTONDRAMARO Hanitra
An ongoing research on the vector X of destinations
5th QATEM 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
5th QATEM 3
• 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
5th QATEM 4
•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
1. Portfolio management applied to tourism
5th QATEM 5
•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)
1. Portfolio management applied to tourism
5th QATEM 6
•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
1. Portfolio management applied to tourism
5th QATEM 7
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
1. Portfolio management applied to tourism
5th QATEM 8
•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
2. Vector X optimization and preference theory
5th QATEM 9
•Expected return for a particular portfolio which includes assets with • number of assets in portfolio p, • proportion of the asset in the portfolio p • and expected return of the asset
•Variance for a particular portfolio with • covariance between return of asset and return of asset
2. Vector X optimization and preference theory
5th QATEM 10
•Following Jang and Chen (2008), the MPT can be formulated as follows for assets:
• and represent respectively • lower and • upper limits • of (proportion of asset i)
2. Vector X optimization and preference theory
5th QATEM 11
•Three levels of risk aversion () are taken in consideration: • = 2 • = 3 higher level of A represents more risk aversion • = 4
• The utility function can be written as follows with expected return and variance of returns
2. Vector X optimization and preference theory
5th QATEM 12
•The optimum value of is computed by solving the following quadratic program:
• and represent respectively • lower and
•upper limits •of (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
5th QATEM 14
3. Application to France with European tourists overnight stays
5th QATEM 15
•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
3. Application to France with European tourists overnight stays
5th QATEM 16
•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)
5th QATEM 17
3. Application to France with European tourists overnight stays
5th QATEM 18
•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
